Percent Error Calculator

Compare a measured or experimental value with the accepted (theoretical) value to see how far off it is as a percentage — the standard accuracy check in chemistry and physics labs.

The textbook, reference or true value you're comparing against.

Percent error
≈ 1.8519%
Signed percent error
≈ -1.8519%measured value is too low
Absolute error
0.05|experimental − theoretical|
Relative error
≈ 0.018519absolute error ÷ |theoretical|
  • Step 1, find the error: experimental − theoretical = 2.65 − 2.7 = -0.05.
  • Step 2, take the absolute value (drop any minus sign): |-0.05| = 0.05.
  • Step 3, divide by the size of the theoretical value: 0.05 ÷ 2.7 ≈ 0.018519.
  • Step 4, multiply by 100: 0.018519 × 100 ≈ 1.8519%.
  • Some teachers keep the sign to show whether the result was too high (+) or too low (−); that's the signed percent error above.

What percent error measures

Percent error tells you how close a measurement is to the accepted value, as a percentage of that accepted value. It's a measure of accuracy: a smaller percent error means your result landed closer to the true value. Lab manuals typically define it as the absolute difference between the experimental and true values, divided by the true value, times 100.

The accepted value comes from a reliable reference — a handbook value, a defined constant or a value calculated from theory. Always divide by the accepted value, not your measurement; dividing by the wrong number is the most common mistake.

Absolute value or signed?

The usual formula uses absolute value bars, so percent error is never negative: you're reporting how far off you were, not which way. Some courses keep the sign, so a negative result means the measurement was too low and a positive one means it was too high. This calculator shows both; check which your instructor or lab manual expects.

Percent error assumes there is a known correct value. When you're comparing two measurements and neither is the "true" one, use percent difference instead: the gap divided by the average of the two values. The percent change calculator shows percent difference alongside percent change.

Reporting the result

Round the percent error to a sensible number of significant figures, usually two or three — the inputs rarely justify more. A percent error says nothing about precision (how close repeated measurements are to each other); you can be precise but inaccurate if your equipment has a consistent bias.

Percent error formula

Percent error = |experimental − theoretical| ÷ |theoretical| × 100
  • experimental = the value you measured or calculated
  • theoretical = the accepted, true or reference value (can't be 0)
  • | | = absolute value (ignore the minus sign)

Worked example: measuring a density

  1. You measure a density of 2.65 g/cm³; the accepted value is 2.70 g/cm³.
  2. Error: 2.65 − 2.70 = −0.05. Absolute error: 0.05.
  3. Relative error: 0.05 ÷ 2.70 ≈ 0.018519.
  4. Percent error: 0.018519 × 100 ≈ 1.85%. Your measurement was 1.85% too low.

Frequently asked questions

Can percent error be negative?

With the standard formula, no — the absolute value makes it positive. If your course uses the signed version, a negative percent error means your measured value was below the accepted value.

What is a good percent error?

It depends on the experiment and equipment. There's no universal cutoff; your lab manual or instructor will usually say what's acceptable for a given procedure.

What's the difference between percent error and percent difference?

Percent error compares a measurement with a known accepted value and divides by that value. Percent difference compares two values with no accepted value and divides by their average. For 2.65 and 2.70, percent error is about 1.85% but percent difference is about 1.87%.

Why divide by the theoretical value and not the experimental one?

Because the error is measured relative to the truth. Dividing by your own measurement would make the same mistake look smaller when you measured high and larger when you measured low.

What if the theoretical value is zero?

Percent error is undefined, because you can't divide by zero. Report the absolute error instead.

Sources

Last reviewed for 2026. How we calculate.