Calculator Tools
Percent Error Calculator
Calculate percent error, signed percent error, percent difference, or solve for an experimental value with the formula and a worked equation shown.
Calculator mode
Compare an experimental measurement to a known accepted value. Always non-negative.
Formula: |experimental - accepted| / |accepted| * 100
Your measured or computed result.
The textbook or reference value you are comparing against.
Worked examples
Tap any example to load it into the calculator. Each one is a standard textbook problem from chemistry, physics, or basic measurement.
Which formula should I use?
- Percent error: use when one of the two values is the accepted, theoretical, or published value and the other is your experimental measurement. This is the formula taught in introductory chemistry and physics and the one most homework problems expect.
- Signed percent error: use the same calculation but keep the sign when direction matters, for example when calibrating an instrument that consistently reads high or low.
- Percent difference: use when neither value is the truth and you simply want to compare two measurements (two rulers, two scales, two lab partners). The formula is symmetric, so swapping the inputs does not change the answer.
- Solve for experimental: use to compute the acceptable range around an accepted value for a given tolerance, for example a calibration spec or a quality control band.
Common rules and pitfalls
- Percent error is always non-negative. If your answer is negative, you are using the signed formula or have swapped the numerator.
- The denominator uses the absolute value of the accepted result. Without the bars, a negative accepted value would flip the sign.
- If the accepted value is zero, percent error is undefined. Switch to absolute error or report the raw difference.
- Percent error and percent difference are not the same thing. Picking the wrong one is the most common grading deduction on chemistry and physics lab reports.
- Significant figures travel with the inputs, not the percent. Report the percent to as many digits as your least precise measurement justifies.
How to use
- Pick a mode at the top: Percent error, Signed percent error, Percent difference, or Solve for experimental.
- Enter the two numbers in the input fields. Percent error and signed percent error take experimental and accepted values; percent difference takes two measurements; solve mode takes the accepted value and the target percent.
- Read the answer in the result panel along with absolute error, relative error, direction (over- or underestimate), and the worked equation.
- Click Copy on any row, or Copy summary to grab a clean breakdown for your lab report or notes.
- Tap a worked example below to load a canonical chemistry or physics problem and see the formula in action.
About this tool
Percent Error Calculator computes the four error figures that lab reports, chemistry problem sets, physics homework, and engineering tolerance specs ask for, with the equation rendered next to every answer so you can see the math, not just the number. Use Percent error when you have an experimental measurement and a known accepted value (the classic chemistry and physics formula, always reported as a non-negative percent). Use Signed percent error when direction matters and a positive answer means too high while a negative answer means too low (the version used to characterize a consistently biased instrument). Use Percent difference when neither value is the accepted truth and you simply want to compare two measurements (two rulers, two scales, two lab partners), with the symmetric formula that gives the same answer regardless of which value you label A or B. Use Solve for experimental to invert the formula: given an accepted value and a target percent error, the calculator returns the high and low experimental values that hit that tolerance, which is the calculation calibration techs run when specifying acceptable measurement bands. Every mode reports the absolute error (the raw difference between the two values), the relative error as a decimal (so you can see what the percent rounded from), and the underlying equation in plain text so you can paste it directly into a lab notebook. Worked examples covering free-fall gravity (9.74 versus 9.81 m/s^2), water density (0.998 versus 1.000 g/mL), sodium chloride molar mass (58.0 versus 58.44 g/mol), and a 100 g standard with 5 percent tolerance load with one click. Inputs accept comma or period decimals, scientific notation like 6.022e23, and negative numbers. The math is deterministic IEEE 754 floating-point arithmetic done locally; nothing you type is sent to a server, so confidential lab data, exam-review numbers, and pre-publication measurements stay on your device.
Free to use. Works in your browser. No signup, no login.
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