This calculator finds the percent error (also called relative error) between a measured value and the accepted true value. It tells you how accurate your measurement was — the smaller the percent error, the closer you were to the real value. The result is always non-negative because the formula uses the absolute difference.
How to Use This Calculator
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Enter the true (accepted) value — the theoretical or reference value you are comparing against.
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Enter the observed (measured) value — the result you actually got.
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Read the percent error and the absolute error below.
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The Direction field tells you whether your measurement was an overestimate or underestimate.
What Is Percent Error?
Percent error is the relative difference between a measured value and the known true value, expressed as a percentage of the true value. A percent error of 0% means your measurement was perfect; a percent error of 10% means you were off by 10% of the true value.
Example: you estimate the width of a room to be 4.8 m, but the actual width is 5.0 m. The percent error is |4.8 − 5.0| / 5.0 × 100 = 0.2 / 5.0 × 100 = 4%. You underestimated by 4%.
Percent error is always expressed as a non-negative number. The direction of the error (overestimate or underestimate) is shown separately by the sign of (observed − true).
Percent Error Formula
The formula divides the absolute difference by the absolute true value, then multiplies by 100 to convert to a percentage.
% error = |OV − TV| / |TV| × 100
where OV = observed value and TV = true value
Worked Example: Speed of Sound
The true speed of sound in air at 20 °C is 343 m/s. In an experiment, you measure 329 m/s.
Step 1 — absolute error: |329 − 343| = 14 m/s
Step 2 — divide by the true value: 14 / 343 ≈ 0.04082
Step 3 — convert to percentage: 0.04082 × 100 ≈ 4.082%
The percent error is 4.082%. Because 329 < 343, this is an underestimate — the measured speed was too low.
Worked Example: Gravitational Acceleration
The accepted value of gravitational acceleration is 9.80665 m/s². A pendulum experiment gives 9.5 m/s².
Step 1 — absolute error: |9.5 − 9.80665| ≈ 0.30665
Step 2 — divide: 0.30665 / 9.80665 ≈ 0.03127
Step 3 — percentage: 0.03127 × 100 ≈ 3.127%
This is a reasonable result for a simple pendulum lab. Typical sources of error include measuring the string length incorrectly or timing fewer than 20 swings.
Percent Error vs. Related Concepts
| Concept | Reference point | Signed? | Typical use |
|---|---|---|---|
| Percent error | Known true value | No (always positive) | Comparing a measurement to a theoretical value |
| Percent difference | Average of both values | No (always positive) | Comparing two values with no known reference |
| Percent change | Starting value (V1) | Yes (positive or negative) | Showing growth or decline over time |
| Standard error | Sample statistics | No | Describing how well a sample represents a population |
Common Sources of Percent Error
Instrument calibration: a scale that reads 2 g too high on every measurement introduces systematic error. The percent error depends on the true value — a 2 g offset on a 10 g sample is a 20% error; on a 200 g sample it is just 1%.
Human error: reading a graduated cylinder from the wrong angle (parallax error), rounding measurements too aggressively, or stopping a timer late all inflate the percent error.
Environmental factors: temperature changes, air currents near a balance, or vibrations in the lab can all shift observed values away from the true value.
To reduce percent error, repeat the measurement multiple times and average the results, use better-calibrated instruments, and control environmental conditions as much as possible.
The percent error calculator computes the relative difference between a measured value and the accepted true value. Enter the true value and your observed measurement to get the percent error instantly.