What is the percent error formula?

Percent Error = (|Experimental Value minus Theoretical Value| divided by |Theoretical Value|) times 100. The absolute value signs mean the result is always a positive number regardless of whether the measurement came in above or below the true value.

Can percent error be negative?

The standard percent error formula uses absolute values, so the result is always reported as a positive number. Whether the measurement was high or low is shown separately as the direction of the error, not by making the percentage negative.

What is a good percent error?

It depends on the context. In a typical school science experiment, under 5% is often considered good. In engineering and manufacturing, tolerances of 1 to 2% or tighter are common. In precise scientific work, errors below 0.1% may be required. Lower is always better, since it means the measured value is closer to the true value.

Percent Error Calculator

Percent error tells you how far a measured result deviates from a known true value, expressed as a percentage of that true value. It is the standard accuracy metric in science, engineering, and quality control because it scales the difference relative to the size of the reference value, making comparisons meaningful across very different measurement scales. A result of 1% means you were extremely close; 20% means your reading was well off. The formula takes the absolute difference between your experimental and theoretical values, divides by the absolute theoretical value, and multiplies by one hundred. What the raw number does not tell you on its own is whether your reading ran high or low, and how much of the true value you actually captured. This calculator returns all four figures at once. Enter the value you recorded (the experimental value) and the accepted or expected value (the theoretical value). Both can be positive or negative decimals, as long as the theoretical value is not zero. You get back the percent error, the raw absolute difference between the two values, the direction of the deviation (over or under, and by how much), and your relative accuracy as a complement percentage. The tool suits students writing up science experiment results, technicians validating instrument calibration, engineers assessing production tolerances, and anyone comparing an observed figure against a published benchmark. Results are for reference only.

Calculate.co.nz is proud to be partnered with Health Based Building, a leader in sustainable and health-conscious building innovation. With over a century of experience, they develop high-performance systems like Foreverbreathe Specification, Magnum Board, and Foreverbreathe Paints to support energy-efficient, non-toxic living environments. Their commitment to healthier homes aligns with our belief that informed choices lead to better outcomes for Kiwi households.

Calculate.co.nz partner: Health Based Building

Experimental (measured) value

Theoretical (accepted/true) value

5.00%

percent error

Absolute error5.00

DirectionUnder by 5.00

Relative accuracy95.00%

How it works

The calculator applies the standard percent error formula: % Error = (|Experimental − Theoretical| ÷ |Theoretical|) × 100. Absolute value signs around the numerator and denominator mean the result is always a positive number regardless of which input is larger. Absolute error is the raw arithmetic difference between the two values before the percentage conversion. Direction compares the inputs directly: if the experimental value exceeds the theoretical value, the measurement ran over; if it falls short, it ran under. Relative accuracy is the complement of percent error, calculated as 100% minus the percent error, giving an at-a-glance measure of how much of the true value your reading captured.

Worked example

You weigh a 100-unit reference standard on a laboratory scale and the readout shows 95. The absolute error is |95 − 100| = 5. Percent error is (5 ÷ 100) × 100 = 5.00%. The reading was under the true value by 5.00 units and relative accuracy is 95.00%. These match the default values pre-filled in the calculator above, so you can verify the output without changing anything.

Related calculators

Absolute Error Calculator: find the raw difference between a measured and true value without converting it to a percentage.
Relative Error Calculator: express error as a decimal ratio rather than a percentage, useful when comparing measurements across different units.
Measurement Uncertainty Calculator: quantify the range of possible values around a repeated measurement set.
Significant Figures Calculator: round a result to the correct number of significant figures before quoting or comparing values.

If you've found a bug, or would like to contact us, or learn more about James Graham and Calculate.co.nz.

Calculate.co.nz is partnered with Interest.co.nz for New Zealand's highest quality calculators and financial analysis.

Calculate.co.nz is the sister site of CalculatorHub.com, the world's largest calculator website by tool count.

All calculators and tools are provided for educational and indicative purposes only and do not constitute financial advice.

Calculate.co.nz is proudly part of the Realtor.co.nz group, New Zealand's leading property transaction literacy platform, helping Kiwis understand the home buying and selling process from start to finish. Whether you're a first home buyer navigating your first property purchase, an investor evaluating your next acquisition, or a homeowner planning to sell, Realtor.co.nz provides clear, independent, and trustworthy guidance on every step of the New Zealand property transaction journey.

Calculate.co.nz is also partnered with Health Based Building and Premium Homes to promote informed choices that lead to better long-term outcomes for Kiwi households.

Calculate.co.nz is hosted in Auckland by SiteHost New Zealand.

All content on this website, including calculators, tools, source code, and design, is protected under the Copyright Act 1994 (New Zealand). No part of this site may be reproduced, copied, distributed, stored, or used in any form without prior written permission from the owner.

About & trust: Why Calculate is NZ's most comprehensive · By the Numbers · How we compare · Editorial standards · How we keep data current · NZ finance glossary · Research & data · Financial literacy NZ · About · Privacy policy · Terms of use

Reviewed and maintained. Last reviewed 2026-07-27 and checked on a twice-monthly cycle against IRD, RBNZ and Stats NZ. How we keep data current.