Percent Error Calculator

Suppose you measure the acceleration due to gravity in a lab and get 9.95 m/s², while the accepted value is 9.81 m/s². Your measurement is close, but how close? The percent error answers exactly that: it is about 1.43%, meaning your reading is off by roughly one and a half percent of the true value. Percent error turns a raw gap between numbers into a single, comparable accuracy score - which is why it is the standard way to report how good an experimental measurement is.

The percent error formula

Percent error compares a measured (experimental) value with a known accepted (actual) value:

In words: subtract the actual value from your experimental value, take the absolute value of that difference, divide by the absolute value of the actual value, and multiply by 100. The absolute value bars are what guarantee a non-negative answer - percent error measures size, not direction.

Experimental value vs actual value

Two terms drive every percent error calculation, and mixing them up is the most common mistake:

• Experimental value - what you actually measured or observed. Also called the measured or observed value. This is the number that may contain error.
• Actual value - the known, correct figure you are comparing against. Also called the true, theoretical, or accepted value (for example a textbook constant or a certified standard). This goes in the denominator.

The accepted value always sits in the denominator. That is what makes percent error meaningful: it expresses the error as a fraction of the thing you are trying to measure correctly.

How to use this percent error calculator

You only need two numbers. Work through the fields in order:

1. Experimental value: type the value you measured or recorded in your experiment.
2. Actual value: type the known accepted, true, or theoretical value you are comparing against.
3. Read the result instantly: the large number at the top is your percent error. Below it you get the absolute error, the signed error (so you know whether you measured too high or too low), the relative error as a decimal, and an accuracy rating.
4. Check the steps: the step-by-step card shows the subtraction, the division, and the multiply-by-100 so you can copy the working into a lab report.

Both fields are editable and the result recalculates the moment you change a number - no button to press.

Worked example 1: measuring gravity

You measure g = 9.95 m/s² and the accepted value is 9.81 m/s².

• Absolute error: |9.95 − 9.81| = 0.14
• Divide by actual: 0.14 ÷ 9.81 = 0.01427
• Multiply by 100: 0.01427 × 100 = 1.43%

A 1.43% error is excellent for a hands-on gravity experiment, and the positive signed error tells you the apparatus read slightly high.

Worked example 2: a chemistry density

You calculate a sample's density as 2.65 g/cm³ but the reference value for the material is 2.70 g/cm³.

• Absolute error: |2.65 − 2.70| = 0.05
• Divide by actual: 0.05 ÷ 2.70 = 0.01852
• Multiply by 100: 1.85%

Here the signed error is negative (you measured low), but percent error reports the magnitude, 1.85% - still very good accuracy.

Worked example 3: a larger gap

A timing experiment gives 48 seconds against an expected 50 seconds.

• Absolute error: |48 − 50| = 2
• Divide by actual: 2 ÷ 50 = 0.04
• Multiply by 100: 4%

Four percent is acceptable for many classroom experiments but large enough that repeating the run and averaging would be worthwhile.

Reference table: common percent errors

This table shows how the experimental value, the actual value, the absolute error, and the resulting percent error relate. Use it to sanity-check your own numbers:

Notice that the same absolute error means a bigger percent error when the actual value is small - which is why context matters when you judge a result.

What counts as a "good" percent error?

• Under 1% - excellent, typical of careful, well-calibrated measurements.
• 1% to 5% - good; acceptable for most school and field experiments.
• 5% to 10% - fair; usable but worth checking your method.
• Over 10% - high; usually signals a systematic error worth investigating.

These bands are general guidelines. Precision physics may demand errors below 0.1%, while a rough field estimate might tolerate 15%. Always interpret percent error against the expectations of your specific task.

Absolute error, relative error, and percent error

These three quantities are closely linked and often confused:

• Absolute error = |experimental − actual|. The raw gap, in the same units as your measurement.
• Relative error = absolute error ÷ |actual|. A unitless decimal that scales the gap by the size of the true value.
• Percent error = relative error × 100. The relative error expressed as a percentage - the most readable form.

Because they are multiples of one another, all three carry the same information; percent error is simply the easiest to compare at a glance.

Tips for accurate calculations

• Put the accepted value in the denominator - never the experimental value.
• Keep units consistent between the two values before subtracting.
• Carry extra digits through the calculation and round only at the end to avoid rounding error.
• Use the signed error when you need to know the direction (too high or too low), and percent error when you only care about magnitude.
• Repeat and average measurements to shrink random error before you compute percent error.

Common pitfalls

Most wrong percent error answers come from a small number of avoidable slips:

• Swapping the denominator - dividing by the experimental value instead of the actual value changes the answer.
• Forgetting the absolute value - this can produce a misleading negative result and break comparisons.
• Dividing by zero - percent error is undefined when the actual value is 0; use absolute error instead.
• Mixing up percent error and percent yield or percent difference - they use different denominators and answer different questions.

Related concepts

Percent error sits in a family of comparison measures. Knowing which to reach for keeps your reporting honest:

• Percent difference compares two measured values when neither is "correct," dividing by their average instead of an accepted value.
• Percent change measures growth or decline from an old value to a new value over time.
• Percent yield (chemistry) compares actual product to theoretical product, where higher is better.
• Standard deviation and uncertainty describe the spread and confidence of repeated measurements, complementing the single-number percent error.

For everyday percentage math - finding X% of Y, percentage increase, or "what percent is A of B" - the Percentage Calculator handles those directly.