Engineering tools / industrial inclination
Inclinometer calculators.
Scale an analog signal, convert tilt into slope and height, or estimate apparent static tilt from horizontal acceleration. Start with an example, then edit the assumptions.
Read the methods and worked examples ↓Results update locally as you type. An attached snapshot changes only when you click Attach again; clearing or switching tools does not change your inquiry. Calculations are not stored in a URL or browser storage.
Methods / reviewed 9 November 2026
Three calculations; three different engineering questions.
Use these tools to prepare controller scaling and application discussions. They solve the stated equations with your inputs; they do not measure an angle, calibrate an instrument or confirm a supplied configuration. Keep the transfer function, installation geometry and motion model explicit when comparing results.
| Question | Use | Confirm separately |
|---|---|---|
| What current or voltage represents this angle? | Linear analog scaling | Actual transfer function, polarity and PLC input range |
| What height component or gradient corresponds to tilt? | Geometry and slope | Length definition, reference stability and installed geometry |
| How could horizontal acceleration disturb a static reading? | Apparent static tilt | Real sensor filtering, motion profile and fusion behavior |
1. Linear analog output scaling.
For angle endpoints θ₀ and θ₁ mapped to signals s₀ and s₁, the assumed relationship is s = s₀ + (θ − θ₀) × (s₁ − s₀) / (θ₁ − θ₀). Endpoints define the scale; units remain mA or V. The calculation accepts an increasing angle interval and either increasing or decreasing signal endpoints. Values outside the stated range are rejected rather than extrapolated.
| Angle | Span position | Calculated current |
|---|---|---|
| −30° | 0% | 4 mA |
| 0° | 50% | 12 mA |
| +15° | 75% | 16 mA |
| +30° | 100% | 20 mA |
The inverse relationship is θ = θ₀ + (s − s₀) × (θ₁ − θ₀) / (s₁ − s₀). For that example, 16 mA corresponds to +15°. This arithmetic does not include ADC error, sensor nonlinearity, supply effects or fault signaling. Verify both channel maps for a dual-axis analog sensor.
A servo-style output may follow a different relationship. The Jewell LSO datasheet describes a sine-related output; applying angle-linear scaling to such a signal requires a documented conversion. A familiar connector or similar range does not establish interchangeability.
Review static analog and digital inclination options →
2. Tilt, slope and vertical height.
With θ in radians, gradient is tan(θ), slope in mm/m is 1000 × tan(θ), and grade in percent is 100 × tan(θ). Degrees convert to radians using θrad = θdeg × π / 180. Do not confuse one degree with one percent grade.
| Known length | Signed height h | Other length |
|---|---|---|
| Physical rigid beam L | L × sin(θ) | Horizontal H = L × cos(θ) |
| Horizontal projection H | H × tan(θ) | Physical L = H / cos(θ) |
At +30° with a 1,000 mm physical beam, height is +500 mm and horizontal projection is approximately 866.025404 mm. With a 1,000 mm horizontal projection at the same angle, height is approximately +577.350269 mm. The difference is geometry, not instrument error.
At +0.005°, a 1,000 mm physical beam has an ideal height component of approximately +0.087266 mm. For change between two readings of that same rigid beam, use Δh = L × [sin(θ₂) − sin(θ₁)]. A real structural network also needs a stable baseline, attachment model and uncertainty analysis. Near ±90°, tangent-based values become highly sensitive to angle, so inspect the length definition carefully.
Plan structural monitoring geometry and network topology →
3. Apparent static tilt from horizontal specific force.
The simplified model holds the device truly level and its measured vertical component at +1 g. If the horizontal specific-force component is x g, the apparent angle is atan(x) × 180 / π. Positive and negative signs follow the chosen measurement axis. Vehicle kinematic acceleration can have the opposite sign to the sensor’s specific-force convention.
| Horizontal component | Apparent angle |
|---|---|
| 0 g | 0° |
| +0.01 g | +0.572939° |
| +0.1 g | +5.710593° |
| −0.1 g | −5.710593° |
The comparison angle reverses this equation: x = tan(θcomparison). For 0.1°, the equivalent component is approximately 0.001745 g under these assumptions. This is an illustrative equivalent component, not an allowable acceleration specification.
Analog Devices AN-1057 explains gravity-based inclination and how additional acceleration disturbs it. Filtering introduces a response tradeoff. Gyroscope fusion adds information but does not make all transient or sustained acceleration disappear. Dynamic inclinometer evaluation should use a defined motion profile, latency and recovery criteria.
Digits, arcseconds and measurement uncertainty.
One degree is 3,600 arcseconds: 0.001° equals 3.6 arcseconds. The conversion follows the angular-unit relationships in NIST’s SI guide, Table 6. Results are rounded for display; calculations use the input numbers. Display precision is separate from resolution, absolute accuracy, temperature behavior and calibration uncertainty.
Request those quantities under the intended bandwidth and temperature conditions. For geometry, include length uncertainty and reference movement in the error budget. For PLC scaling, include sensor, input module and conversion errors. This page assigns no numerical uncertainty to an actual installation.
Confirm the output law → define length and mounting references → describe motion → specify acceptance conditions. Attach the relevant calculation below, then add the actual required range, accuracy and interface.
Send calculation context with an RFQ ↓Questions before using a result.
Can I use this for both 4–20 mA and voltage outputs?
Yes, if the documented output is linear with angle. Set both angle and signal endpoints, then select mA or V. Negative voltage endpoints and reversed signal spans are supported. The calculator does not verify loop resistance, supply headroom, analog-input impedance or fault-current bands.
Does zero angle always mean 12 mA?
Only for a symmetric bipolar angle range mapped linearly to 4–20 mA. For a 0°–90° range, zero is 4 mA and 45° is 12 mA. Confirm zero settings, axis polarity and scaling after installation.
Can I calculate a 0°–360° output?
You can evaluate one continuous interval up to 360°. A physical wrap at 360°/0° needs the device’s endpoint convention and controller handling. This tool does not simulate wrap transitions, dead zones or multi-turn position.
Why are sine-output inclinometers different?
Some analog instruments output a signal proportional to the sine of angle. A linear-angle mapping then gives the wrong intermediate values even when endpoints appear similar. Use the manufacturer’s transfer function and calibration coefficients for that model.
Is the height result bridge settlement?
It is the ideal vertical component for one length and angle. Settlement or deflection needs a baseline, reference stability, sensor spacing and a validated geometric model. A tilt reading alone cannot distinguish reference movement, local bending and rigid-body rotation.
What does 0.001° mean in arcseconds?
It equals 3.6 arcseconds; 0.0005° equals 1.8 arcseconds. Neither number alone defines absolute accuracy or calibration uncertainty. More calculator digits do not improve a sensor’s measurement capability.
Does a 0.1 g input prove a dynamic sensor will err by 5.71°?
No. That number comes from the stated ideal static model: true level, +1 g vertical and 0.1 g horizontal specific force. A fused instrument’s response depends on its algorithm, bandwidth, motion history and installation, which this calculator does not model.
Can I derive a machine alarm or hydraulic shutoff limit here?
No. These calculations do not define stability margins, certified safety functions, braking behavior or load-dependent limits. Provide the machine duty cycle and control requirements for a separate system review.
Will editing a calculator change an attached RFQ?
An explicit Attach action copies the current valid inputs into a read-only snapshot. Later edits leave it unchanged until you attach again. You can remove it without clearing your contact details, technical requirements or notes.
What should I send after calculating?
Send the documented transfer function, required axes and range, supply, interface, response time, temperature and mounting conditions. For mobile equipment add acceleration duration and vibration data. Use the calculation as context and request a model-specific review.
Continue with the inclinometer versus accelerometer working guide for sensing and calibration, or request model-specific drawings and protocol files from engineering resources.
Calculation → configuration review
Send the assumptions with your application requirements.
Keep the calculation as context, then state your actual range, accuracy, motion and mounting needs separately. A result does not select or qualify an ICS model.