Percent Error Calculator: Formula, Absolute vs Relative Error + Lab Examples — ToolMars Blog

Q: What is the percent error formula?

Percent error = |experimental − theoretical| / |theoretical| × 100. Absolute values keep the result positive so you report magnitude of error, not direction.

Q: What is the difference between absolute error and relative error?

Absolute error is |experimental − theoretical| in the same units as the measurement. Relative error is absolute error divided by |theoretical|; percent error is relative error × 100.

Q: Can percent error be negative?

With the absolute-value formula used in most labs and this calculator, percent error is reported as a non-negative percentage. Some courses ask for signed error to show over- or underestimation — check your instructions.

Q: What if the theoretical value is zero?

You cannot divide by zero. Percent error relative to a zero accepted value is undefined; report absolute error instead or use a different reference your instructor specifies.

Q: Is a lower percent error always better?

Generally yes for accuracy vs a known standard — but very low error can also reflect lucky cancellation or an oversimplified model. Discuss precision, systematic bias, and significant figures in your lab write-up.

Percent error tells you how far an experimental result sits from an accepted or theoretical value — as a percentage of that reference. A free percent error calculator applies the standard lab formula so you can focus on interpreting the result, not arithmetic slips.

This guide walks through the formula, absolute vs relative error, and worked science examples you can reuse in lab reports.

Compute percent error from experimental & theoretical values

Free percent error calculator — lab-ready formula, instant and private.

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Percent Error Formula

The form used in most chemistry and physics labs is:

% error = |experimental − theoretical| / |theoretical| × 100

Absolute values make the percentage positive. “Experimental” is what you measured; “theoretical” (or accepted) is the reference value from a textbook, data sheet, or known constant.

Absolute Error vs Relative Error

Absolute error = |experimental − theoretical| (same units as the measurement)
Relative error = absolute error / |theoretical| (unitless)
Percent error = relative error × 100 (a percentage)

A 0.5 g absolute error looks huge on a 2 g sample but tiny on a 500 g sample — relative and percent error put the mistake in context.

Lab Science Examples

Worked calculations

Density: measured 7.85 g/cm³ vs accepted 7.87 → |7.85−7.87|/7.87 × 100 ≈ 0.25%
Boiling point: measured 98.2 °C vs 100.0 °C → |98.2−100|/100 × 100 = 1.8%
Gravity lab: measured 9.65 m/s² vs 9.81 → |9.65−9.81|/9.81 × 100 ≈ 1.63%
Verify any pair with the ToolMars percent error calculator.

Tips for Lab Reports

State which value is experimental and which is theoretical, keep units consistent, and report an appropriate number of significant figures. Discuss possible systematic sources (calibration, parallax, heat loss) — a small percent error still deserves a short explanation of method quality.

Compute percent error from experimental & theoretical values

Free percent error calculator — lab-ready formula, instant and private.

Calculate Percent Error Now

Frequently Asked Questions

What is the percent error formula?

|experimental − theoretical| / |theoretical| × 100.

What is the difference between absolute error and relative error?

Absolute error is the raw difference; relative error divides that by |theoretical|; percent error is relative × 100.

Can percent error be negative?

The absolute-value formula yields a non-negative percentage; some courses want signed error instead.

What if the theoretical value is zero?

Percent error is undefined — do not divide by zero; report absolute error or another metric.

Is a lower percent error always better?

Usually it means closer agreement with the standard — still analyze precision and bias in your write-up.