Percent Error
Compare experimental and theoretical values with % error = |E − T| / |T| × 100, relative error, and signed deviation. Free online calculator with formulas and step-by-step solutions.
Key formula
% error = |E - T| / |T| × 100
How do you calculate percent error?
Use % error = |experimental − theoretical| / |theoretical| × 100. The absolute value makes the percent non-negative. A signed form (E − T) / T × 100 keeps the direction: positive means the measurement was high.
About this tool
Percent error tells a lab how far a measured value sits from the accepted value, as a percentage of that accepted value. This page keeps % error = |E − T| / |T| × 100 visible so reports do not mix it up with ordinary percents or percent difference.
How to use this calculator
- Choose the correct mode or direction before entering numbers.
- Make sure your values match the expected units or date format shown in the fields.
- Calculate once, then read both the final output and the supporting formula steps.
- Round only after you understand the result so you do not lose useful precision too early.
Worked examples
Example 1: 9.7 vs 9.8 m/s²
E = 9.7, T = 9.8. |E − T| = 0.1. % error = 0.1 / 9.8 × 100 ≈ 1.02%. Signed = (9.7 − 9.8) / 9.8 × 100 ≈ −1.02%.
Example 2: 99.2 °C vs 100 °C
E = 99.2, T = 100. % error = |99.2 − 100| / 100 × 100 = 0.80%.
Example 3: 0.89 vs 0.79 g/cm³
E = 0.89, T = 0.79. % error = 0.10 / 0.79 × 100 ≈ 12.7%. A large percent error usually means units, identity, or method — not just rounding.
Frequently asked questions
What is the percent error formula?
% error = |E − T| / |T| × 100, where E is experimental and T is theoretical (accepted). Relative error is the same ratio without multiplying by 100.
Can the theoretical value be zero?
No. The formula divides by T. If the accepted value is zero, percent error is undefined; report the absolute difference instead and follow your lab’s rule.
What is the difference between percent error and percent difference?
Percent error uses the accepted value in the denominator. Percent difference uses the average of two measurements when neither is the true value: |A − B| / ((A + B)/2) × 100.
Should percent error be negative?
Unsigned percent error is ≥ 0 because of the absolute value. Signed percent error can be negative when E is below T. Use whichever form the rubric asks for.
Do units cancel in percent error?
Yes, if E and T share the same unit. Convert first, then subtract. The percent itself is unitless.