Accelerometer Voltage & g Calculator
Convert analog accelerometer output voltage into signed acceleration using zero-g bias and mV/g sensitivity. The calculator also predicts output voltage, solves calibration points, checks range limits and estimates ADC g-per-code references.
SEN-009 is intentionally a one-axis voltage transfer-function tool. Tilt, roll, pitch, vector magnitude, IMU fusion and dynamic motion estimation belong to separate sensor calculators.
Engineering tool
Accelerometer Voltage & g Calculator
Convert analog accelerometer voltage to signed acceleration, predict output voltage, calibrate zero-g bias and sensitivity, and estimate ADC g-per-code references.
Calculation mode
Parameter panel
Result console
- Acceleration
- 1 g
- Acceleration
- 9.80665m/s²
- Voltage Offset from Zero-g
- 300 mV
- Direction
- Positive Acceleration
- Measured Output Voltage
- 1.95 V
- Range Status
- Within Linear Output Range
The sign is preserved. Do not take absolute value unless your application deliberately ignores axis direction. The g used here is acceleration, not grams of mass.
Accelerometer voltage and g formula audit
| Adopted Linear Model | VOUT = VZERO + S × a_g. |
|---|---|
| Axis Polarity Convention | Signed acceleration follows the sensor axis definition; negative values are preserved. |
| Zero-g Voltage Definition | VZERO is the sensor output when acceleration projection on that axis is 0 g. |
| Sensitivity Definition | S is output-voltage change per g of acceleration. |
| Sensitivity Units | µV/g, mV/g and V/g are converted internally to V/g. |
| Standard Gravity Constant | 1 g = 9.80665 m/s². |
| Voltage → g Formula | a_g = (VOUT - VZERO) / S. |
| g → Voltage Formula | VOUT = VZERO + S × a_g. |
| Zero Offset Formula | a_offset = (Vzero,measured - Vzero,nominal) / S. |
| Single-Point Sensitivity Solver | S = (V - VZERO) / a; known acceleration cannot be 0 g. |
| Two-Point Calibration | S = (V2 - V1)/(a2 - a1), VZERO = V1 - S×a1. |
| +1g / -1g Calibration | S = (Vplus - Vminus)/2 and VZERO = (Vplus + Vminus)/2. |
| Range Model | Endpoint voltages are predicted from the same linear transfer function. |
| Saturation Policy | Predicted voltages outside output limits are flagged and not clamped. |
| ADC Resolution Reference | g/code = VLSB / |S × analog gain|. |
| Tolerance Corner Model | a=(V-Vzero)/S is recalculated at bounded voltage and sensitivity corners. |
| Temperature Drift Boundary | Optional drift uses a first-order linear reference only. |
| Stationary 1g Boundary | A stationary axis aligned with gravity can read about ±1 g; still does not mean every axis is zero-g. |
| Noise / Bandwidth Boundary | ADC g/code is not noise floor or dynamic bandwidth accuracy. |
| SEN-010 Scope Boundary | Tilt, roll, pitch and vector magnitude belong to the future accelerometer tilt/vector calculator. |
Formula reference
Accelerometer Voltage and g Formulas
The adopted first-order model treats analog accelerometer output as a signed linear voltage transfer function around zero-g bias.
VOUT = VZERO + S × a_ga_g = (VOUT - VZERO) / Sa_m/s² = a_g × 9.80665a_offset = (Vzero,measured - Vzero,nominal) / SS = (V2 - V1) / (a2 - a1)+1g/-1g: S = (Vplus - Vminus) / 2+1g/-1g: VZERO = (Vplus + Vminus) / 2g/code = VLSB / |S × G|Variable definitions
- VOUT
- measured accelerometer output voltage
- VZERO
- zero-g output voltage
- S
- sensitivity in volts per g
- a_g
- signed acceleration in g
- G
- optional analog gain before an ADC
- VLSB
- ADC input voltage per code
Accelerometer Voltage & g Formula Audit
| Adopted Linear Model | VOUT = VZERO + S × a_g. |
|---|---|
| Axis Polarity Convention | Acceleration is signed according to the sensor axis direction. |
| Zero-g Voltage Definition | VZERO is the output voltage when gravity or acceleration projection on that axis is 0 g. |
| Sensitivity Definition | S is output voltage change per g of acceleration. |
| Sensitivity Units | µV/g, mV/g and V/g are converted to internal V/g. |
| Standard Gravity Constant | 1 g = 9.80665 m/s². |
| Voltage → g Formula | a_g = (VOUT - VZERO) / S. |
| g → Voltage Formula | VOUT = VZERO + S × a_g. |
| g ↔ m/s² Conversion | a_m/s² = a_g × 9.80665. |
| Zero Offset Formula | a_offset = (Vzero,measured - Vzero,nominal)/S. |
| Single-Point Sensitivity Solver | S = (V - VZERO)/a; a must not be 0. |
| Two-Point Calibration | S = (V2 - V1)/(a2 - a1), VZERO = V1 - S×a1. |
| +1g / -1g Calibration | S = (Vplus - Vminus)/2, VZERO = (Vplus + Vminus)/2. |
| Range Model | Endpoint voltages are predicted from acceleration min/max without clamping. |
| Saturation Policy | Out-of-range predicted output is flagged as saturation likely. |
| ADC Resolution Reference | g/code = VLSB / |S × G|. |
| Tolerance Corner Model | The inverse formula is recalculated at bounded V, VZERO and S corners. |
| Temperature Drift Boundary | Optional drift is a first-order reference, not a full thermal model. |
| Stationary 1g Boundary | A stationary accelerometer can read ±1 g on an axis aligned with gravity. |
| SEN-010 Scope Boundary | Tilt, roll, pitch and vector magnitude are intentionally out of scope. |
Worked Examples
Voltage to +1 g
Known: VZERO=1.65 V, S=300 mV/g, VOUT=1.95 V
a=(1.95-1.65)/0.3=+1 g.
Voltage to -1 g
Known: VOUT=1.35 V with same zero and sensitivity
a=(1.35-1.65)/0.3=-1 g.
+2 g output
Known: a=+2 g, VZERO=1.65 V, S=0.3 V/g
VOUT=1.65+0.3×2=2.25 V.
-2 g output
Known: a=-2 g, VZERO=1.65 V, S=0.3 V/g
VOUT=1.05 V.
Standard gravity
Known: 1 g
1 g = 9.80665 m/s².
Two g in SI units
Known: 2 g
2 g = 19.6133 m/s².
SI to g
Known: 9.80665 m/s²
a=1 g.
Zero offset
Known: Nominal zero=1.65 V, measured zero=1.68 V, S=0.3 V/g
Offset=0.03/0.3=+0.1 g ≈0.980665 m/s².
Single-point sensitivity
Known: Known +1 g, V=1.95 V, VZERO=1.65 V
S=(1.95-1.65)/1=0.3 V/g.
Invalid single-point
Known: Known acceleration=0 g
Rejected because sensitivity slope is undefined.
Two-point calibration
Known: -1 g→1.35 V, +1 g→1.95 V
S=0.3 V/g, VZERO=1.65 V.
+1g/-1g sensitivity
Known: Vplus=1.95 V, Vminus=1.35 V
S=(1.95-1.35)/2=0.3 V/g.
+1g/-1g zero
Known: Vplus=1.95 V, Vminus=1.35 V
VZERO=(1.95+1.35)/2=1.65 V.
Duplicate calibration acceleration
Known: a1=a2
Rejected because two-point slope is undefined.
±2 g output span
Known: VZERO=1.65 V, S=0.3 V/g
Output range is 1.05 V to 2.25 V.
Saturation warning
Known: VCC/output max=2.0 V, predicted +2 g output=2.25 V
The unclamped model is shown and saturation is flagged.
No clamping
Known: Predicted output=2.25 V outside 2.0 V limit
Result remains 2.25 V for engineering review.
12-bit ADC LSB
Known: 0-3.3 V ADC
VLSB=3.3/4096≈805.664 µV.
ADC g per code
Known: S=300 mV/g, 12-bit 0-3.3 V
g/code≈0.00268555 g ≈2.68555 mg.
ADC SI per code
Known: Same ADC setup
m/s² per code≈0.02634 m/s².
Sensitivity unit
Known: 300 mV/g
Equals 0.3 V/g.
Round trip
Known: a=-0.75 g to voltage and back
Recovered acceleration remains -0.75 g before display rounding.
Engineering Notes
| Accelerometer | An accelerometer measures proper acceleration or specific force, not only motion through space. |
|---|---|
| Analog Accelerometer | Many analog accelerometers map axis acceleration into a proportional output voltage. |
| Zero-g Bias | Zero-g output is an offset voltage, not necessarily 0 V. |
| Sensitivity | Sensitivity is often specified as mV/g and may vary with supply, part tolerance and temperature. |
| Standard Gravity | The calculator uses 9.80665 m/s² to avoid hidden 9.8 rounding assumptions. |
| Positive / Negative Axis | Axis polarity comes from the package orientation and datasheet axis diagram. |
| Ratiometric Output | If the device is ratiometric, use zero-g bias and sensitivity at the actual supply condition. |
| Offset Error | Zero offset error directly becomes acceleration error through a_offset=ΔVZERO/S. |
| Sensitivity Error | Sensitivity error changes measurement scale and should be included in calibration or tolerance checks. |
| Calibration | A +1g/-1g orientation test can estimate both sensitivity and zero-g output for one axis. |
| ADC Resolution | g/code is a quantization reference and does not include sensor noise or ADC nonlinearity. |
| Noise Density | Noise can make practical acceleration resolution worse than one ideal ADC code. |
| Bandwidth | Dynamic measurements depend on accelerometer and analog front-end bandwidth. |
| Cross-Axis Sensitivity | Acceleration on one physical axis can create smaller output on another axis in real devices. |
| Temperature Drift | Zero-g bias and sensitivity may drift with temperature and should be checked in the datasheet. |
Common Mistakes
- Treating g as grams instead of acceleration.
- Using 9.8 m/s² without documenting the standard-gravity convention.
- Entering mV/g as if it were V/g.
- Forgetting to subtract zero-g voltage before dividing by sensitivity.
- Taking the absolute value of negative acceleration and losing axis direction.
- Assuming zero-g output is always VCC/2.
- Assuming a stationary sensor means every axis is at 0 g.
- Reversing the +1g/-1g calibration equations.
- Trying to solve sensitivity from a 0 g point.
- Calling ADC g/code total acceleration accuracy.
- Ignoring output swing or sensor saturation limits.
- Ignoring temperature offset and sensitivity drift.
- Ignoring sensor noise, bandwidth and cross-axis sensitivity.
- Adding tilt calculation here instead of using a dedicated tilt/vector model.
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FAQ
How do I calculate acceleration from accelerometer voltage?
Subtract the zero-g voltage from the measured output voltage, then divide by sensitivity in volts per g: a = (VOUT - VZERO)/S.
How do I calculate accelerometer output voltage from g?
Use the linear model VOUT = VZERO + S × a, where S is sensitivity in V/g and a is signed acceleration in g.
What does mV/g mean?
mV/g means millivolts of output change per g of acceleration. A 300 mV/g sensor changes output by 0.3 V for each 1 g along the measured axis.
What is zero-g bias?
Zero-g bias is the output voltage when the acceleration projection on that sensor axis is 0 g. It is often near mid-supply for single-supply sensors, but not always.
Why is zero-g output often near half the supply voltage?
Many analog accelerometers are single-supply and need headroom for positive and negative acceleration, so the zero-g output is commonly biased near mid-supply.
How many m/s² are in 1 g?
Standard gravity is defined as exactly 9.80665 m/s² for this calculator.
What does negative acceleration mean?
Negative acceleration means the measured acceleration projection is opposite the sensor axis positive direction. The calculator preserves this sign.
Why can a stationary accelerometer read 1 g?
An accelerometer measures proper acceleration or specific force. At rest, an axis aligned with gravity can read approximately +1 g or -1 g depending on orientation.
How do I calibrate accelerometer zero offset?
Use a true zero-g condition for that axis or a +1g/-1g orientation method. Do not assume simply sitting still means 0 g on every axis.
How do I calibrate accelerometer sensitivity?
Use a known non-zero acceleration point with a trusted zero-g value, or use two known acceleration points and solve the voltage slope.
How does the +1g / -1g calibration method work?
Measure output at +1 g and -1 g on the same axis. Sensitivity is (Vplus - Vminus)/2 and zero-g bias is (Vplus + Vminus)/2.
How do I calculate accelerometer resolution with an ADC?
Find the ADC voltage LSB, divide it by effective sensitivity in V/g, and the result is the ideal g per ADC code.
Is ADC g-per-code the same as accelerometer accuracy?
No. ADC g-per-code is only quantization resolution. Accuracy also depends on sensor noise, offset, sensitivity error, bandwidth, ADC errors and calibration.
How does temperature affect zero-g bias?
Datasheets may specify zero-g temperature coefficient. A first-order estimate is ΔVZERO = TCzero × ΔT, then Δg = ΔVZERO/S.
What is cross-axis sensitivity?
Cross-axis sensitivity is unwanted response from acceleration along a different physical axis. This calculator does not model that behavior.
How does accelerometer bandwidth affect measurement?
Bandwidth limits dynamic acceleration response and noise. This calculator uses a static linear voltage model and does not predict frequency response.
What is the difference between this calculator and an accelerometer tilt calculator?
This calculator converts analog output voltage to signed acceleration on one axis. Tilt, roll, pitch and vector magnitude belong to the future Accelerometer Tilt & Vector Calculator.