Percent Error Calculator

Percent error: |measured − theoretical| / |theoretical| · 100%

Percent error tells you how far an experimental result strays from a reference value: E% = |x_meas − x_ref| / |x_ref| · 100%. Absolute error keeps the original units, but the percentage version scales with the quantity, so you can put measurements of wildly different magnitudes side by side. A 1 mm error means a lot on a 10 mm length and almost nothing on 1 km. Take g_measured = 9.7 m/s² against g_ref = 9.81 m/s²: that works out to E% = |9.7 − 9.81|/9.81 · 100% ≈ 1.12%. One caveat — the formula falls apart when the reference is exactly zero, so reach for absolute error there, or normalize against some characteristic scale instead.

Applications

You see it in school and undergraduate physics lab reports, in instrument calibration (thermometers, balances, manometers), and when numerical models get checked against experiment (CFD, FEM, finite differences). It also shows up in analytical-method validation at INMETRO/ABNT NBR ISO/IEC 17025 labs, in quality control for pharmaceutical assays, and whenever simulation codes are cross-validated against benchmark problems.

FAQ

Percent error vs relative error vs percent difference? Percent error treats one value as "correct" (the reference). Relative error is the same fraction, just without the ×100. Percent difference is what you use when neither number gets to be the "truth" — it compares two equally trusted values via |a − b| / ((a+b)/2) · 100%.

Should I take the absolute value? If you mean "error" as a magnitude, yes. But when the sign carries information — say you care whether the measurement sits above or below the reference — report the signed error instead: (x_meas − x_ref)/x_ref · 100%.

What is an "acceptable" percent error? That really depends on the field. Undergraduate physics usually expects < 5%. In engineering, FEM/CFD compared against experiment lands somewhere around 5–15%. Analytical chemistry methods often demand < 2%. Whatever the number, judge it against the propagated uncertainty.