Percentage Error Calculator
Calculate the percentage error and absolute error between a measured and true value.
KNOWN/ACCEPTED VALUE PRESETS
What Is the Percentage Error Calculator?
This percentage error calculator computes the unsigned percentage error, signed error (indicating over/underestimate direction), absolute error, and relative error between a measured and accepted value. Built-in presets load common physical constants as the theoretical value.
- ›Percentage error: The primary result, how far off the measurement is, as a percentage of the true value.
- ›Signed error: Positive means overestimate (measured too high); negative means underestimate.
- ›Accuracy rating: Colour-coded classification from Excellent (<0.1%) to Very Poor (≥20%).
- ›Known value presets: Speed of light, gravitational acceleration, π, Avogadro's number, and more.
- ›Scientific notation support: Handles very large and very small values correctly.
Formula
| Metric | Formula | Meaning |
|---|---|---|
| % Error | |Exp − Theo| / |Theo| × 100 | Unsigned, magnitude of error |
| Signed % Error | (Exp − Theo) / |Theo| × 100 | Positive = overestimate, negative = underestimate |
| Absolute Error | |Exp − Theo| | Raw difference from true value |
| Relative Error | |Exp − Theo| / |Theo| | Fraction of theoretical value |
How to Use
- 1Optionally click a preset to load a known theoretical value.
- 2Enter the experimental (measured) value.
- 3Enter the theoretical (accepted/true) value, or use the preset loaded value.
- 4Press Enter or click Calculate Error.
- 5Read the percentage error, accuracy rating, absolute error, and signed error.
- 6Click Clear to reset.
Example Calculation
Measuring gravitational acceleration in a lab
% Error vs % Difference
Understanding Percentage Error
What Is Percentage Error?
Percentage error quantifies the accuracy of a measurement by expressing the deviation from the true value as a percentage of that true value. It is always positive (unsigned) and indicates how large the error is relative to the scale of the measurement. A 0.01% error on a length measurement means the measured value deviates by 1 part in 10,000 from the true value.
Error Classification
| % Error | Rating | Typical context |
|---|---|---|
| < 0.1% | Excellent | High-precision instruments, calibration labs |
| 0.1–1% | Very Good | Good laboratory technique |
| 1–5% | Good | Standard lab experiments |
| 5–10% | Acceptable | Introductory physics / rough measurements |
| 10–20% | Poor | Significant systematic or random error |
| ≥ 20% | Very Poor | Likely equipment failure or calculation error |
Sources of Experimental Error
- ›Systematic error: consistent offset in one direction, instrument miscalibration, parallax, friction
- ›Random error: unpredictable scatter around the true value, reduced by averaging repeated measurements
- ›Human error: incorrect reading, wrong unit, arithmetic mistake
- ›Environmental: temperature, humidity, vibration affecting the measurement apparatus
Frequently Asked Questions
What is the formula for percentage error?
% Error = |Experimental − Theoretical| / |Theoretical| × 100
The absolute values ensure the result is always positive and works for negative theoretical values.
What is the difference between percentage error and percentage difference?
Percentage error compares a measurement to a known true value using the true value as the base. Percentage difference compares two measured values using their average as the base:
Use % error when one value is an established standard (g = 9.807, c = 299,792,458 m/s). Use % difference when both values are measurements of equal standing with no true reference.
What does the signed percentage error tell me?
The signed error = (Experimental − Theoretical) / |Theoretical| × 100. Positive means your measurement was higher than the true value (overestimate); negative means it was lower (underestimate). This reveals systematic bias:
- ›Consistently positive: your instrument reads too high (add a correction factor)
- ›Consistently negative: your instrument reads too low
- ›Randomly positive/negative: random error, reduce by averaging more trials
Why use |Theoretical| in the denominator instead of |Experimental|?
The theoretical (accepted) value is the reference standard, it represents what we believe is true. Dividing by it normalises the error against the scale of the true quantity. If we divided by the experimental value, a wild measurement would inflate the denominator and make a large error appear small. Using the true value as base gives a consistent, meaningful scale.
What is absolute error vs relative error?
Absolute error is the raw difference |Exp − Theo| in the same units as the measurement. Relative error is that difference divided by the true value (dimensionless). Percentage error is relative error expressed as a percentage:
Relative error is preferred when comparing measurements across different scales. Absolute error matters when the physical magnitude of the deviation is what counts.
How do I reduce percentage error in an experiment?
- ›Calibrate instruments before use and compare to known standards
- ›Repeat measurements and average, reduces random error by √n
- ›Use a longer pendulum or larger sample to make the signal bigger relative to error
- ›Control environmental variables (temperature, vibration)
- ›Use more precise instruments (more decimal places, smaller divisions)
- ›Eliminate systematic bias by checking measurement method against known values
Can percentage error be greater than 100%?
Yes, percentage error is not bounded at 100%. If the theoretical value is 1 and you measured 3, the error is |3−1|/1 × 100 = 200%. This would indicate a very large error, typically suggesting a wrong order of magnitude, an incorrect unit, or an equipment failure rather than a typical measurement uncertainty.