How to Calculate Percent Error: Lab Formula |E − T| / |T| × 100

Calculate percent error with |experimental − theoretical| / |theoretical| × 100. Worked lab examples, signed error, and a free percent error calculator.

What Percent Error Asks

Percent error compares a measured (experimental) value to an accepted (theoretical) value. Labs use it to report how far a result sits from the known answer, as a percentage of that accepted value.

The usual school formula is % error = |E − T| / |T| × 100. E is experimental, T is theoretical. Absolute value makes the percent error non-negative; a signed form keeps the direction (too high or too low).

If you already have E and T and only need a checked percent, open the free percent error calculator first, then return here for the denominator rule and percent-difference trap.

The Formula

% error = |E − T| / |T| × 100 — magnitude, always ≥ 0.

Signed % error = (E − T) / T × 100 — positive means E is larger than T.

Relative error = |E − T| / |T| — the same ratio without × 100.

T in the denominator is the accepted / true / theoretical value, not the average of E and T. Mixing that with percent difference is the most common lab-report mistake.

Percent Error vs Percent Difference

Percent difference compares two measurements of the same kind when neither is the accepted value: |A − B| / ((A + B)/2) × 100. Use percent error only when one number is the accepted theory, textbook, or known constant.

Ordinary part-whole percents (not lab error) belong on the percentage calculator.

Units and Rounding

E and T must use the same unit before you subtract (both m, both °C, both N).

The % error itself is unitless (a percent).

T cannot be zero — you cannot divide by the accepted value.

Round the reported percent using your lab’s significant-figure rules. Check digit count with the significant figures calculator.

Worked Examples

Example 1: g lab, 9.7 vs 9.8

E = 9.7 m/s², T = 9.8 m/s². |E − T| = 0.1. % error = 0.1 / 9.8 × 100 ≈ 1.02%. Signed: (9.7 − 9.8)/9.8 × 100 ≈ −1.02% (slightly low).

Example 2: boiling point, 99.2 °C vs 100 °C

E = 99.2, T = 100. % error = |99.2 − 100| / 100 × 100 = 0.80%.

Example 3: density, 0.89 g/cm³ vs 0.79 g/cm³

E = 0.89, T = 0.79. % error = 0.10 / 0.79 × 100 ≈ 12.7%. Large percent error usually means a method, unit, or identity mix-up — not just rounding.

Common Mistakes

Putting E in the denominator instead of T.

Using the average of E and T (that is percent difference).

Leaving E and T in different units.

Dropping the absolute value when the rubric wants unsigned percent error.

Calling a huge percent error “close enough” without checking the setup.

Check It on the Calculator

Percent error calculator — |E − T| / |T| × 100.

Percentage calculator — part, whole, and percent change.

Significant figures calculator — rounding for lab reports.

Learn % error = |E − T| / |T| × 100, then confirm every lab number on the calculator.

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