How to Calculate Percent Error

Percent error tells you how far a measured or experimental value sits from the true or accepted value, expressed as a percentage. It is one of the most common calculations in science labs because it turns a raw gap into a number you can compare across experiments, instruments, and units. A gap of 0.16 grams per cubic centimetre means nothing on its own, but 2 percent instantly signals a tight, high-quality measurement.

How do you calculate percent error step by step?

Subtract the true value from your measured value, drop the sign, divide by the true value, then multiply by 100. The four steps below always work, whether you are measuring density, the acceleration due to gravity, or the concentration of a solution.

1. Subtract the theoretical (true) value from your experimental value.
2. Take the absolute value, so the result is positive.
3. Divide by the theoretical value (not by your measured value).
4. Multiply by 100 to get a percentage.

The single most common slip is dividing by the wrong number. The denominator is always the accepted or true value, because that is the reference you are comparing against. Dividing by your own measurement gives a different, non-standard figure that will not match a textbook answer key.

What does a worked percent error example look like?

Suppose the accepted density of a substance is 8.00 grams per cubic centimetre and you measured 7.84. Follow the four steps and you land on a 2 percent error, which is a strong result for a school lab.

1. Difference: 7.84 minus 8.00 equals minus 0.16.
2. Absolute value: 0.16.
3. Divide by the true value: 0.16 divided by 8.00 equals 0.02.
4. Multiply by 100: 2 percent error.

Notice that the measurement came out below the true value, giving a negative difference, but the final percent error is still positive. That is the whole point of the absolute value step. If you want to keep the direction of the gap, you are computing relative error instead, which is covered further down.

Where is percent error used in real experiments?

Percent error shows up anywhere a measurement has a known accepted value to check against. In chemistry it grades a measured density, a molar mass from an experiment, or the percent yield of a reaction. In physics it checks a value for the acceleration due to gravity, a spring constant, or the speed of sound against the textbook figure. Because the result is a single percentage, a teacher can compare a density lab and a gravity lab on the same scale even though the raw units are completely different.

Here is a second worked example from a classic physics lab. The accepted acceleration due to gravity is about 9.81 metres per second squared. A pendulum experiment gives 9.62. Running the same four steps returns roughly a 1.9 percent error, which is a solid result for hand timing.

1. Difference: 9.62 minus 9.81 equals minus 0.19.
2. Absolute value: 0.19.
3. Divide by the true value: 0.19 divided by 9.81 equals 0.0194.
4. Multiply by 100: about 1.9 percent error.

What is a good percent error?

In a typical school science lab a percent error under about 5 percent is usually considered good, and under 10 percent is acceptable. There is no universal cutoff, because the acceptable range depends entirely on the field, the equipment, and the size of the quantity being measured. A precision analytical balance is expected to land well under 1 percent, while a rough kitchen-scale experiment might reasonably sit near 10 percent.

A large percent error is a signal, not a verdict. It usually points to one of three things: a measurement problem such as parallax or a miscalibrated instrument, a flawed method or procedure, or a mistake in the accepted value you are comparing against. The U.S. National Institute of Standards and Technology treats every measurement as having some uncertainty, and its guidance on measurement uncertainty is the standard reference for how far a result can reasonably stray from the accepted value.

What causes percent error: systematic or random?

Percent error rolls two very different problems into one number, and knowing which one you are facing is what lets you fix it. Systematic error is a consistent bias that pushes every reading in the same direction, such as a scale that is not zeroed, a stopwatch started late every time, or reading a meniscus from the wrong angle. Random error is scatter that pushes readings both above and below the true value, such as reaction time or small fluctuations in the environment. The two behave differently when you repeat the measurement.

• Systematic error stays the same size and direction on every trial, so repeating the measurement will not reveal it. You fix it by calibrating the instrument or correcting the method.
• Random error changes from trial to trial and tends to cancel out, so averaging several readings pulls the result closer to the true value.
• A high percent error with tight, repeatable readings points to systematic bias. A high percent error that jumps around each trial points to random noise.

This is also why a low percent error does not automatically prove your method was sound. Two systematic errors can cancel by luck and hand you a small number, so treat percent error as one piece of evidence rather than a final grade on the experiment.

How is percent error different from relative and percent difference?

These three are easy to mix up. Percent error compares a measurement to a known true value. Relative error is the same calculation without the absolute value, so it keeps a plus or minus sign and can be negative. Percent difference compares two experimental values when neither is the accepted truth.

• Percent error: absolute gap from a known true value, always positive. Use it when a textbook or accepted value exists.
• Relative error: signed gap from the true value, can be negative. Use it when the direction of the error matters.
• Percent difference: gap between two measurements divided by their average. Use it when comparing two trials with no accepted value. See percent difference explained for the full formula.

Because all three share the same skeleton, people often reach for the wrong one. If there is a single accepted answer, you want percent error. If you are comparing two of your own readings against each other, you want percent difference.

Common mistakes to avoid

• Dividing by the experimental value instead of the true value. The denominator is always the accepted value.
• Forgetting the absolute value and reporting a negative percent error. Percent error is reported as a positive number.
• Mixing up units before subtracting. Convert both values to the same unit first, or the difference is meaningless.
• Multiplying by 100 twice, or forgetting it entirely, so the answer is off by a factor of 100.
• Rounding too early. Keep full precision until the final step, then round once.

Calculate it instantly

Enter your experimental and true values below and the calculator returns the percent error with the steps. For related work you can also use the percentage calculator or brush up with how to calculate a percentage.