Summary: A tilt sensor and a vibration accelerometer are usually the same MEMS sensing element with a different specification written around it. The tilt instrument is a direct current device: one degree of tilt near level is 17.45 milligrammes of acceleration, so the published 0.005 degree accuracy of a structural inclinometer is a claim about 87 microgrammes, and its datasheet is written around zero stability rather than bandwidth. The vibration instrument is specified for the alternating end of the spectrum and is often alternating current coupled, which physically removes the gravity term and makes it incapable of reporting an attitude at any price. The deciding question is therefore not which instrument is better but where the phenomenon sits in frequency: below roughly 0.1 hertz it is a tilt question, between 0.1 and 150 hertz it is both, and above that it is a vibration question.
1. Two Instruments, One Sensing Element
Almost every tilt sensor on the market is an accelerometer. The element inside it is a small proof mass on a compliant silicon structure, and what that element responds to is acceleration. The reason it can report an angle is that when the sensor is standing still, the only acceleration acting on it is gravity, and gravity has a known direction and a known magnitude. The angle is a geometric calculation performed on where the gravity vector lands on the sensing axes. There is no separate physical principle at work.
A vibration sensor uses the same element and the same physics. What separates the two instruments is not what they sense but which end of the frequency axis their specification was written for. Vibration work starts at a few hertz and extends upward into the hundreds and thousands. Tilt work starts at zero hertz, because that is where a structure that is not currently moving sits.
That difference has a hard version, and it settles some cases on its own. Accelerometers come in two electrical classes. An alternating current response device, which is almost always piezoelectric, has a coupling capacitor or an equivalent high pass time constant in its signal path. That high pass removes the direct current component, and the direct current component is exactly the part that carries gravity. The consequence is not a loss of accuracy or a smaller number. It is that such a device cannot measure static acceleration at all, and therefore cannot report an attitude at any price, with any amount of averaging, or with any subsequent signal processing. The transducer selection literature states this without qualification: an alternating current coupled device cannot be used to measure static acceleration such as gravity, and is only suitable for measuring dynamic events.
The second class is direct current response, coupled down to zero hertz, and it can therefore see gravity. Capacitive MEMS elements and piezoresistive elements are the usual technologies in this class, and this is precisely why tilt sensors are built around them. A tiltmeter is a direct current accelerometer whose specification has been written around the zero hertz end.
| Family | Coupling | Where the specification is written, and what that buys | What it cannot report |
| Tilt sensor | Direct current, down to zero hertz | At the low end: zero deviation, zero temperature drift, resolution expressed in degrees. Gravity is the reference, so the reading is an absolute attitude rather than a relative change | Any motion faster than its internal averaging, and no amplitude or phase response is published to predict what it will do |
| Vibration accelerometer | Alternating current, with a high pass corner set by the coupling | At the high end: frequency range, noise density in microgrammes per root hertz, sensitivity in millivolts per g, and the mounted resonance | Any absolute attitude. Gravity was removed by the coupling, so tilt is not a poor reading here, it is an absent one |
One further class sits between the two and is worth naming. A direct current response accelerometer with a wide full scale, chosen for shock or vibration measurement, is electrically capable of reading gravity. It is simply not specified in a way that makes the reading useful, and the sections that follow show why in numbers.
2. A Tilt Reading Is an Acceleration in Disguise
Near level, the acceleration that a tilt sensor sees along one axis is the sine of the tilt angle multiplied by g. The practical consequence is a single constant that the accelerometer application literature publishes in its own tables: one degree of tilt is 17.45 milligrammes of acceleration. The same source gives the resolution an accelerometer needs in order to see a given inclination step, and the numbers are worth carrying in your head: 0.1 degree needs 1.745 milligrammes, 0.25 degree needs 4.363, 1 degree needs 17.45, and 2 degrees needs 34.9. Anyone comparing a tilt specification against an acceleration specification is working with these numbers whether they realise it or not.
| Tilt step | Equivalent acceleration | What the same figure means for a tilt instrument |
| 0.001 deg | 17.5 microgrammes | The published resolution of the RS485 structural inclinometer and of the NB-IoT geotechnical tiltmeter |
| 0.005 deg | 87.3 microgrammes | The published typical accuracy of the RS485 structural inclinometer over its 15 degree range |
| 0.01 deg | 175 microgrammes | The same accuracy specification at its maximum |
| 0.05 deg | 873 microgrammes | The published zero deviation of the same instrument |
| 0.1 deg | 1.745 milligrammes | The resolution an accelerometer needs in order to see a tenth of a degree |
| 1 deg | 17.45 milligrammes | The resolution an accelerometer needs in order to see one degree |
| 15 deg | 259 milligrammes | The full range of the RS485 structural inclinometer, expressed as acceleration |
| 30 deg | 500 milligrammes | The full range of the NB-IoT geotechnical tiltmeter |
Read that table in the other direction and it becomes a statement about procurement. A specification written as plus or minus 0.005 degrees is a claim about 87 microgrammes. At that size the analogue to digital converter is never the limiting term, and the zero almost always is.
Two further consequences follow from the sine, and both of them show up in the datasheets as design decisions rather than as footnotes.
The first is that the sensitivity is not constant. Differentiating the sine gives the cosine, so a degree of tilt moves the reading by 17.45 milligrammes near level and by that figure multiplied by the cosine of the angle further up: about 15.1 milligrammes at 30 degrees, a loss of about 13 percent, and about 8.7 milligrammes at 60 degrees, exactly half. This is why tilt instruments are sold in ranges of plus or minus 5, 15 and 30 degrees rather than in units of g. The range states how far the sine is still well conditioned, not how hard the instrument can be shaken.
Written as acceleration, the whole published tilt family fits inside a single g: plus or minus 5 degrees is 87 milligrammes, plus or minus 15 degrees is 259 milligrammes, plus or minus 30 degrees is 500 milligrammes, and the widest range offered, plus or minus 90 degrees, is exactly 1 g. A tilt instrument never needs a wider range than that, and the narrowness is the point. A narrow span is also the easier place to build a stable zero, and as a later section shows, span and zero stability are not independent.
The second consequence is the one that explains most field surprises. Because gravity and every other acceleration enter through the same channel, a direct current offset that is not gravity is indistinguishable from gravity. The same application note works a published example: a dual axis solution with perfect sensitivity but a 50 milligramme offset on one axis reports an angle error of about 2.9 degrees, and the sign of the error changes with the quadrant. A 50 milligramme offset is not a fault. It is an ordinary zero drift on a part that was never specified for attitude.
3. The Low End: What a Tilt Datasheet Is Really Specifying
The published specification of the RS485 structural monitoring inclinometer shows what a serious low end specification looks like. It is a dual axis instrument with a plus or minus 15 degree range, read over Modbus RTU at 9600 bits per second, supplied from 8 to 36 volts and drawing 15 to 20 milliamperes at 24 volts, in an aluminium case rated IP67 and operating from minus 40 to plus 85 degrees Celsius. It carries EMC and CE compliance and an explosive atmosphere certification.
The performance block is the part worth reading closely, because every line in it is a statement about the zero hertz end.
| Published line | Value | What the line decides in practice | Equivalent acceleration on the tilt axis at level |
| Resolution | 0.001 deg | The smallest angular change the instrument will report once its output has settled. It is a figure for the slow path and not a noise floor at high frequency | 17.5 microgrammes |
| Accuracy, typical | plus or minus 0.005 deg from 0 to 15 deg | How faithfully the instrument reports a change in angle, measured at room temperature, which is why it is not the line that decides outdoor performance | 87.3 microgrammes |
| Accuracy, maximum | plus or minus 0.01 deg | The worst case the manufacturer will guarantee over the same range at the same temperature | 175 microgrammes |
| Zero deviation | plus or minus 0.05 deg | How far the absolute reading can sit from true zero. It is ten times the accuracy figure, and because it is a fixed offset a baseline subtraction removes it | 873 microgrammes |
| Zero temperature drift | plus or minus 0.002 deg per degree Celsius typical, with a maximum of plus or minus 0.13 deg across the operating range | The line that decides long term outdoor behaviour, because it walks over months rather than scattering over seconds and cannot be cancelled by a baseline recorded on another day | 35 microgrammes per degree Celsius |
| Cross axis error | plus or minus 1 percent | How much tilt on one axis leaks into the reading on the other | Not a single axis quantity |
| Refresh time | 40 milliseconds | How often the instrument will produce a new answer. It is an update rate, not a bandwidth | Not an acceleration figure |
| Power-on startup time | 0.5 second | How long after power is applied before the first valid reading can be trusted | Not an acceleration figure |
The row that deserves a second look is the refresh time. Forty milliseconds is 25 updates per second, which looks like a bandwidth until the note attached to it is read: it is the time the instrument takes to update a biaxial angle value once, and the next angle query should be kept at least that far from the end of the previous one. The line describes how fast the digital channel can be read. It does not describe how faithfully the reported angle follows a structure that is moving. No amplitude response and no phase response are published for this instrument.
That is not a criticism of this datasheet. It is what a tilt datasheet is for. An attitude is a slow quantity, the customer needs the zero to be stable and the resolution to be honest, and a frequency response curve would answer a question that no tilt customer has asked. The practical consequence for anyone comparing the two instrument families is narrower and more awkward: you cannot compute from a tilt datasheet what the instrument will do to a five hertz vibration. That is not a number that was left out. It is a specification the instrument does not carry.
4. The High End: What a Vibration Datasheet Is Specifying
A vibration accelerometer datasheet is a mirror image. It leads with the frequency range and the mounted resonance, gives sensitivity in millivolts per g, gives noise as a spectral density in microgrammes per root hertz, and quotes full scale in g. The direct current terms are usually absent, and where the device is alternating current coupled they cannot exist at all, because the coupling removed the information they would describe.
The mirror image is clearest in the one line both families do publish: the bias, or zero, temperature coefficient. In a tilt instrument that line decides whether the instrument is usable at all. In a vibration instrument it is a curiosity, and the numbers show it.
The published datasheet of an instrumentation grade capacitive MEMS accelerometer family makes the argument better than any reasoning, because the same design is offered across six full scales and the bias temperature coefficient is published for every one of them, as a typical value in each case.
| Full scale | Bias temperature coefficient, typical | The same coefficient expressed as apparent tilt, using 17.45 milligrammes per degree | Coefficient per g of full scale |
| plus or minus 2 g | plus or minus 0.1 milligramme per degree Celsius | 0.0057 degrees of apparent tilt per degree Celsius | 0.050 |
| plus or minus 5 g | plus or minus 0.25 milligramme per degree Celsius | 0.0143 degrees per degree Celsius | 0.050 |
| plus or minus 10 g | plus or minus 0.5 milligramme per degree Celsius | 0.0286 degrees per degree Celsius | 0.050 |
| plus or minus 30 g | plus or minus 1.5 milligrammes per degree Celsius | 0.0859 degrees per degree Celsius | 0.050 |
| plus or minus 50 g | plus or minus 2.5 milligrammes per degree Celsius | 0.1432 degrees per degree Celsius | 0.050 |
| plus or minus 100 g | plus or minus 5 milligrammes per degree Celsius | 0.2865 degrees per degree Celsius | 0.050 |
The last column is the finding, and it is the reason this section belongs in an article about tilt sensors. Every range in that family carries a bias temperature coefficient of about 0.05 milligramme per degree Celsius for each g of full scale. The constant itself is a property of one manufacturer design and not a law of nature, but the direction of the trade is general and it is the whole difficulty: range and zero stability travel together, so a wider range is a proportionally worse attitude reference.
Buying a wider range is exactly what a vibration application demands, because the instrument has to survive the events it is there to record. So the specification that makes an accelerometer good at vibration work is the same specification that makes it poor at tilt work, and there is no trade to be struck in the middle: the two requirements pull the same parameter in opposite directions.
Set that against the tilt instrument. The RS485 inclinometer publishes a typical zero temperature drift of plus or minus 0.002 degrees per degree Celsius, which is 35 microgrammes per degree Celsius. The narrowest instrumentation accelerometer in the family above, at 2 g, publishes plus or minus 0.1 milligramme per degree Celsius, which is 100 microgrammes, about three times larger. The 30 g part that a shock or machine measurement requires publishes plus or minus 1.5 milligrammes per degree Celsius, which is 1,500 microgrammes, about forty three times larger. Both figures are typical values from published datasheets, so they are comparable on the same basis.
One further check removes the last objection. Noise is not what stops an accelerometer from being a tiltmeter. The same 2 g part publishes an in band noise of 7 microgrammes per root hertz, which over a one hertz bandwidth is 7 microgrammes root mean square, and that is 0.0004 degrees of angle. The tilt instrument resolves 0.001 degrees. At these sizes the noise floor of a good accelerometer is finer than the resolution of a good tiltmeter, so the obstacle is not the random term at all. It is the systematic one, the zero, and the zero is set by the range.
5. The Crossover Rule: When an Acceleration Becomes a Tilt Error
Everything so far describes a sensor standing still. Put the same sensor in an environment where it is being pushed, and the direct current channel cannot tell the push from the lean, because the two arrive as the same physical quantity. The apparent tilt from a steady lateral acceleration a is the arctangent of a divided by g, and at these magnitudes it is the same number as the ratio itself.
| Steady lateral acceleration | Apparent tilt it produces | Multiple of the published 0.005 degree accuracy |
| 0.0001 g | 0.0057 deg | 1.1 times |
| 0.0005 g | 0.0286 deg | 5.7 times |
| 0.001 g | 0.0573 deg | 11.5 times |
| 0.005 g | 0.2865 deg | 57.3 times |
| 0.01 g | 0.5729 deg | 115 times |
Read as a steady state, that table is alarming, and every deployment on a moving or loaded structure would be hopeless. What makes it survivable is frequency, and the same arithmetic that creates the table also sets its limits.
A steady component survives averaging intact at any window length. A sinusoidal one does not. Averaging a sine of amplitude A and frequency f over a window of duration T leaves a residual no larger than A divided by the product of pi, f and T. Lengthening the window and raising the frequency both shrink the leak into the angle.
Put the two cases side by side. A steady lateral bias of 0.005 g reports 0.2865 degrees and never goes away. A vibration of 0.5 g at 20 hertz, which is one hundred times larger in acceleration, averaged over a 60 second window leaves at most 0.5 divided by the product of pi, 20 and 60, which is about 0.00013 g, or 0.0076 degrees.
An acceleration one hundred times larger therefore produces about forty times less angle error, and the only thing that differs between the two cases is frequency. This is the single most useful rule in the whole comparison: a tilt channel tolerates enormous fast acceleration and is defenceless against a small steady one.
The rule explains two field observations that otherwise look contradictory. A cover set in a trafficked road can hold a perfectly stable resting angle while vehicles pass over it, because those loads are fast enough to average out inside the reporting interval, and the same cover will show a slow drift when its bedding shifts by a fraction of a degree. A machine frame can read steady while idle and shift its reading when the load comes on, because that load is a steady acceleration in the sensor frame rather than a vibration, and no averaging length will remove it.
There is a corollary worth stating, because the obvious fix is the wrong one. Stretching the averaging window is exactly the right way to reject fast acceleration, and it is also the way to become blind to a fast movement of the structure itself. An averaging filter has no way to distinguish the two, because the two produce the same acceleration. What decides which one you are looking at is whether the angle returns when the excitation stops, and that requires more than one reading in the record.
6. What Each Instrument Cannot See
Stated plainly, the two instruments fail in opposite directions, and the failure of each is invisible in the other datasheet.
The alternating current instrument cannot see gravity. No amount of gain, range selection or post processing recovers it, because the information was removed in the analogue front end before the signal reached the converter. A vibration channel can report the amplitude, the frequency and the duration of an event with great precision and cannot report the attitude the structure is in afterwards. Attempting to obtain attitude or displacement by integrating the acceleration runs into the same wall, and the standard for vibration measurement of fixed structures says so directly: when the signal is low frequency and small in amplitude, the transducer output is so small that the result of integration is affected by integrator noise, the appropriate response is to use a capacitive accelerometer instead, and it is better to measure the required quantity directly than to integrate or differentiate another one.
The tilt instrument has the opposite limit, and it is a deliberate one. It is slow. Its datasheet publishes an update rate, and no published response curve describes how faithfully it follows a moving structure, so a vibration that falls near its internal averaging band cannot be interpreted from the datasheet at all. A resolution of 0.001 degrees is the resolution of the slow path. It is not a noise floor at 20 hertz, and the 0.001 degree figure should not be read across to a dynamic question.
The failure mode of choosing the wrong instrument is therefore not a worse number. It is a missing number, and in practice it is a number that looks plausible enough to be believed, which is why the mistake survives review.
| What you need to know | The quantity it is | The instrument, and the end of the frequency axis its specification is written for | What that instrument will not give you |
| Has the support moved since last year | A very slow change in attitude | A tilt instrument at the zero hertz end, specified by zero drift, zero deviation and resolution | Any event shorter than its averaging window |
| How far has this tower leaned in this wind | A steady lean plus a low frequency oscillation, superimposed | Both channels, and the separation has to be done in the analysis rather than in the instrument | One number that carries both meanings unambiguously |
| What did this machine experience last night | Amplitude and frequency of vibration against time | An accelerometer at the high end, specified by frequency range, noise density and mounted resonance | Whether the machine is still level afterwards |
| What did this shipment experience, and where did it end up | An event record plus an attitude | Two channels, one recording acceleration and one recording angle | Either one alone, when the other is the question being asked |
7. Five Questions That Settle the Choice
The decision does not need a comparison of products. It needs the phenomenon to be placed on the frequency axis first, because every other parameter follows from that placement.
Question one: how fast is the thing you are worried about? Settlement, creep, seasonal movement and thermal deformation live below about 0.01 hertz, which is one cycle per hundred seconds. The response of a pole or a tower to wind sits around 0.1 to 10 hertz. The machinery vibration standard family works in the decade from 10 to 1000 hertz. The standard for vibration of fixed structures covers 0.1 to 500 hertz and notes that most damage from man made sources occurs between 1 and 150 hertz, while natural sources carry their damage level energy between 0.1 and 30 hertz. Name the frequency of your phenomenon before naming an instrument.
Question two: do you need an absolute attitude or a relative one? An absolute attitude requires a direct current channel and a zero that does not walk. A relative one, meaning a change measured against a baseline recorded with the same instrument, is considerably easier, because a fixed offset cancels in the subtraction and only repeatability remains. The published zero deviation of the RS485 inclinometer, at plus or minus 0.05 degrees, is ten times its accuracy figure, and a baseline relative reading is unaffected by it.
Question three: is there a sustained acceleration in the environment? Wind thrust on a tall structure, an unbalanced machine, a vehicle under power and a conveyor carrying a load all produce a steady component that a tilt channel will report as tilt. If the answer is yes, budget either for a second channel or for a reference point that is mechanically isolated from the load path.
Question four: does the record have to be a number or a waveform? An attitude is a number at a point in time and tolerates a long reporting interval. A vibration is a waveform, and the interval that preserves it is much shorter, which changes the power budget as well as the instrument. The distinction is easy to lose because both arrive as a column of numbers in a database.
Question five: what is the smallest movement that matters, expressed in the unit the decision is made in? Convert it to degrees if it is not already, then multiply by 17.45 milligrammes per degree to obtain the acceleration it corresponds to, remembering that the multiplier tightens with the cosine as the angle grows. If the answer comes out at a few tens of microgrammes, the question is a tilt question. If it comes out at hundreds of milligrammes, it is a vibration question, and the two answers will not come from the same part.
8. When You Need Both Channels on One Asset
On real assets the answer is usually both channels, and the reason is that they answer different halves of the same incident. A tilt channel reports that the geometry has changed. An acceleration channel reports what the asset was subjected to. Neither reconstructs the other, and a monitoring specification that names only one of them has left one of the two questions unanswered.
A load in transit is the cleanest example, because the two questions separate completely. The acceleration record answers what the shipment experienced: the amplitudes of the peaks, how long each lasted, and at what frequency. The tilt channel answers whether the load ended up in a different attitude from the one it started in. A large peak that leaves the attitude unchanged is a shipment that survived a rough road. A modest peak that does change the attitude is a shipment that moved on its mountings, and that is the case worth investigating. A single channel reports one of those two and stays silent on the other, and the silent case is the one that ends in a dispute.
The published product families follow the same split. The transportation vibration tester is built around a MEMS acceleration acquisition module with a hardware real time clock and high capacity internal storage, recording vibration and shock events continuously, in a fully sealed housing on a lithium thionyl chloride battery, with a maximum continuous recording duration of more than 180 days. The tilt instruments record an attitude over long intervals on a much smaller power budget. The accelerometer product is a multi axis vibration measurement device with a CAN bus interface, a built in programmable terminal resistor and CANopen support, which is the interface a condition based maintenance system expects.
There is a diagnostic bonus in having both, and it costs nothing once both channels exist. Because a steady acceleration and a real rotation look identical in the angle channel, a time aligned acceleration record lets you attribute a step in the angle to a cause. If the angle step coincides with a large acceleration event, the structure was pushed. If it does not, the structure moved, and the acceleration channel has just ruled out the alternative explanation.
On a structure rather than a shipment the same pairing works across different time scales. The tilt channel carries the months long baseline and the slow rate of change. The acceleration channel is switched into a higher activity mode when something specific happens: a storm, a collision, a change of loading regime, or a maintenance operation that alters the structure. Neither schedule suits the other instrument.
9. The Specification Line That Actually Decides
The comparison ends in two short reading orders, and neither of them puts accuracy first.
For a tilt instrument, read the zero temperature drift first, because it is the term that walks over months and cannot be cancelled by a baseline recorded on a different day. Read zero deviation or zero repeatability second, because a baseline relative reading is limited by how well the zero returns rather than by how accurate the absolute value is. Read resolution third, keeping in mind that it is a figure for the slow path. Read the refresh time last, as an update rate rather than a bandwidth. Accuracy, the line every procurement table quotes first, is measured at room temperature in a room, and it sits below the drift and repeatability lines rather than above them.
For a vibration instrument, read the frequency range first, because a channel that does not cover the frequency of interest cannot answer the question however good its remaining numbers are. Read noise density second, because it sets the smallest signal visible in the bandwidth you actually need. Read full scale and the mounted resonance as a pair third, because a transducer bolted to a flexible bracket has a mounted resonance far below the one printed on its own datasheet, and the resonance is what limits the usable upper frequency.
The transferable rule is this. When two instrument families appear to answer the same question, do not compare their sensing elements, because they are frequently the same element. Compare the end of the frequency axis that each datasheet was written for. The coupling, the range, the presence or absence of a zero stability figure, and the units on the sensitivity line will all follow from that single difference, and in most projects the instrument has effectively been chosen before any product is looked at.
One boundary stays outside this article. Neither instrument decides whether the movement it reports is acceptable. That is a question about criteria, thresholds and the mechanism of failure, and it is answered by the standard governing the structure rather than by the hardware. What the hardware decides is whether the phenomenon of interest appears in the record at all.
Frequently Asked Questions
- Can I use an accelerometer to measure tilt? Yes, if it is a direct current response type with a stable zero and a narrow enough range. One degree of tilt is 17.45 milligrammes of acceleration, so the whole question is whether the part’s zero is stable to a small fraction of a milligramme. A published instrumentation grade 2 g accelerometer has a typical bias temperature coefficient of plus or minus 0.1 milligramme per degree Celsius, which is 0.0057 degrees of apparent tilt per degree Celsius, about three times the drift of a purpose built tiltmeter. An alternating current coupled piezoelectric accelerometer cannot do it at all, because the coupling removes gravity in the analogue front end before any conversion takes place.
- My tilt reading changes when the machine starts. Is the sensor faulty? Almost certainly not, and the reading is probably correct. A steady lateral acceleration of 0.005 g is reported as 0.2865 degrees, which is 57 times the published 0.005 degree accuracy figure, so a load that a machine imposes on its own frame arrives in the angle channel at full size. Check whether the change is steady or transient. If it holds while the machine runs and returns when it stops, it is a quasi static load and the angle channel cannot separate it from a lean. If it disappears when the reporting interval is lengthened, it was fast enough to average out.
- Is a tilt sensor just a low range accelerometer with a different label? The physics is the same and the specification is not. Two lines separate them. The first is the coupling, because a tiltmeter must be direct current coupled to see gravity. The second is the range. In one published instrumentation accelerometer family the bias temperature coefficient scales with full scale at about 0.05 milligramme per degree Celsius per g, so the 30 g part chosen for vibration work carries a zero drift roughly fifteen times that of the 2 g part in the same family. Widening the range to survive vibration is the most direct way to lose the zero that an attitude needs.
- Do I need to convert tilt to acceleration in order to compare the two? Yes, and it is the only way to compare like with like. A tilt specification quoted in degrees and an acceleration specification quoted in milligrammes are not the same kind of statement until one is converted. Use 17.45 milligrammes per degree near level, and multiply by the cosine of the angle as the tilt grows, since the sensitivity falls to about 15.1 milligrammes at 30 degrees and 8.7 at 60. The conversion also runs the other way and is often more useful: a 0.001 g steady acceleration is 0.0573 degrees, so a test bench load or a vehicular acceleration can be expressed directly as the tilt error it will cause.
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