Percent Error Calculator
Free percent error calculator. Compare an experimental (measured) value against a theoretical (actual) value, with step-by-step working.
What is percent error?
Percent error measures how far an experimental (measured) value strays from a theoretical (actual, accepted) value, expressed as a percentage of the theoretical value.
- E (experimental) — what you measured, observed, or estimated.
- T (theoretical) — the accepted, true, or exact value. It always sits in the denominator.
|E − T| equals |T − E| — the subtraction order doesn't change the answer. What matters is that T stays in the denominator, never E.The four steps
- Subtract:
E − T. - Take the absolute value of that difference.
- Divide by T (the theoretical value).
- Multiply by 100 to convert to a percentage.
Worked examples
Boiling point of water. A thermometer reads E = 101.5°C against an accepted T = 100°C.
Candy weight. A bag is labeled T = 10 oz, but weighs E = 10.3 oz on a scale.
The absolute error here is |10.3 − 10| = 0.3 oz — the raw gap before it's turned into a percentage.
Portion size. You scoop E = 30 pieces of candy against a recommended T = 20.
That's 50% more than the recommended amount.
Absolute error vs. relative error vs. percent error
| Quantity | Formula | Units |
|---|---|---|
| Absolute error | |E − T| | same units as the measurement |
| Relative error | |E − T| / T | unitless decimal |
| Percent error | |E − T| / T × 100 | percentage |
Percent error is just the relative error scaled by 100 and labeled with a % sign — all three come from the same underlying difference.
Percent error vs. percentage change
Percent error looks like the Percentage Change formula — both use a (new − base) / base shape. The difference: percent error always takes the absolute value, so it never reports a direction, and its base is specifically the theoretical (expected) value rather than a starting point in time.
Common mistakes
- Dividing by the experimental value. The denominator is always
T(theoretical), neverE. - Forgetting the absolute value. Without it, an experimental value below the theoretical value would report a misleading negative percentage.
- Confusing percent error with percent difference. Percent error compares a measurement to a known correct value; percent difference compares two measurements with no known "correct" answer.
Where percent error shows up
- Science labs — comparing a measured result to a textbook or accepted value.
- Manufacturing and quality control — checking how far a produced part deviates from its spec.
- Everyday estimation — checking how close a guess or forecast came to the actual outcome.
Frequently asked questions
- What is the percent error formula?
- Percent error equals the absolute value of (experimental minus theoretical), divided by the theoretical value, multiplied by 100 — where the theoretical value is the accepted or true value.
- Why is the result always positive?
- The formula takes the absolute value of the difference, so percent error never reports a direction — it only measures how far off a measurement is, not whether it ran high or low.
- Does the order of experimental and theoretical matter?
- Only for which value sits in the denominator. Because of the absolute value, |E − T| always equals |T − E| — the theoretical value must be the divisor either way, or the result is meaningless.
- What is the difference between absolute error and percent error?
- Absolute error is the raw difference |E − T| in the same units as the measurement. Percent error expresses that same gap as a percentage of the theoretical value, which makes it easier to judge how significant the error is.
- What is the difference between percent error and relative error?
- Relative error is the decimal form of the gap, |(E − T) / T|. Percent error is simply the relative error multiplied by 100 and shown with a percent sign.
- What is considered a "good" percent error?
- It depends on the field — a percent error under 1% is typical for careful lab measurements, while everyday estimates can carry a much larger acceptable margin. There is no universal cutoff.
- Can the theoretical value be zero?
- No. Percent error divides by the theoretical value, so a theoretical value of zero makes the formula undefined — there is no percentage to compute against a baseline of zero.