What This Percent Error Calculator Does
This tool compares a value you measured against the value you expected (the true or theoretical value) and tells you how far off your measurement was. It is widely used in chemistry, physics, engineering and lab classes to judge how accurate an experiment or instrument really is. Alongside percent error, it also reports the absolute error and the relative error so you get the full picture from a single calculation.
The Two Inputs You Enter
- Measured value – the result you actually obtained from your experiment, instrument or estimate.
- True (actual/theoretical) value – the accepted, expected or reference value you are comparing against.
Both should be in the same units. The calculator uses the absolute value of the difference and divides by the absolute value of the true value, so the result stays positive even if your true value is negative or your measurement overshoots.
The Formula
The percent error is calculated as:
Percent Error = |Measured − True| ÷ |True| × 100%
The calculator derives three outputs from your inputs:
- Absolute error = |Measured − True|
- Relative error = Absolute error ÷ |True|
- Percent error = Relative error × 100
Worked Example
Suppose you measured the density of a liquid as 1.05 g/mL, while the accepted true value is 1.00 g/mL.
- Absolute error = |1.05 − 1.00| = 0.05 g/mL
- Relative error = 0.05 ÷ 1.00 = 0.05
- Percent error = 0.05 × 100 = 5%
So your measurement was 5% higher than the true value — a small, generally acceptable error for a basic lab.
Interpreting Your Percent Error
Percent error tells you how far a measured value strays from a known true (accepted) value, expressed as a percentage of that true value. The smaller the number, the closer your measurement is to reality.
- Low percent error (near 0%) means your measurement is accurate — it agrees closely with the true value.
- High percent error signals a meaningful discrepancy, which may point to calibration drift, procedural mistakes, environmental interference, or simply using the wrong measurement technique.
Typical Acceptability Thresholds
What counts as "good" depends entirely on the field:
| Context | Typical acceptable percent error |
|---|---|
| Introductory school / chemistry labs | < 5–10% |
| General engineering & applied science | < 2–5% |
| Precision engineering & metrology | < 1% |
| Analytical / pharmaceutical chemistry | often < 0.5% |
As a worked illustration, suppose you measured a density of 2.65 g/cm³ when the true value is 2.70 g/cm³. The percent error is \(\frac{|2.65 - 2.70|}{|2.70|}\times 100\% = \) 1.85% — comfortably within most lab and engineering tolerances.
Accuracy Is Not Precision
Percent error measures accuracy: closeness to the true value. It does not measure precision, which is how repeatable your measurements are with each other. A set of readings can be highly precise (tightly clustered) yet inaccurate (all clustered far from the true value), or accurate on average but scattered. Use percent error for accuracy and statistics like standard deviation for precision.
Magnitude, Not Direction
Because the standard formula uses the absolute value, percent error reflects only the size of the discrepancy, not whether you overestimated or underestimated. A measurement that is 3% too high and one that is 3% too low both yield a 3% percent error. If the direction of the deviation matters, drop the absolute-value bars or use a signed percentage-change calculation instead.
How to Calculate Percent Error by Hand
Follow these steps to compute percent error for any measurement:
- Subtract the true value from the measured value. Compute \(\text{Measured} - \text{True}\) to find the raw error.
- Take the absolute value. Drop any negative sign so the result is positive: \(|\text{Measured} - \text{True}|\). This is the absolute error.
- Divide by the absolute true value. Calculate \(\dfrac{|\text{Measured} - \text{True}|}{|\text{True}|}\). This gives the relative error as a decimal.
- Multiply by 100. Convert the decimal relative error into a percentage.
- Attach the percent sign (%). Label the final number with % to show it is a percent error.
Units must match. The measured and true values must be expressed in the same units before you subtract — for example, both in grams or both in millimeters. Mixing units (such as cm with mm) produces a meaningless result. The units cancel during the division, which is why percent error is a unitless percentage.
Worked Example
A scale reads 48 g for an object whose true mass is 50 g.
- Raw error: \(48 - 50 = -2\) g
- Absolute error: \(|-2| = 2\) g
- Relative error: \(\dfrac{2}{|50|} = 0.04\)
- Multiply by 100: \(0.04 \times 100 = 4\)
- Result: 4%
Frequently Asked Questions
Can percent error be negative? This calculator always returns a positive number because it uses absolute values. It tells you the magnitude of the error, not its direction.
What counts as a good percent error? It depends on the field. In many school labs, under 5–10% is considered acceptable, while precision engineering may require well below 1%.
What if the true value is zero? Dividing by zero is undefined, so percent error cannot be computed when the true value is 0. Use absolute error in that situation instead.
Related percentage calculators
- Percent Change Calculator — increase or decrease from an old value to a new one.
- Percentage Increase Calculator — how much a value went up, in percent.
- Percentage Decrease Calculator — how much a value went down, in percent.
- Percentage Difference Calculator — compare two numbers with no before/after.
