What is the percent error formula?

Percent Error = (|Experimental − Accepted| / |Accepted|) × 100. The absolute value in the numerator ensures the result is always non-negative, so it measures the size of the error regardless of direction.

Why do we use the absolute value?

Taking the absolute value strips the direction (over vs under) from the calculation so the result expresses the magnitude of the error as a pure percentage. The calculator still tells you separately whether your value was above or below the accepted value.

Can the percent error ever be negative?

No. By convention, percent error is always expressed as a non-negative number because the formula uses |Experimental − Accepted|. If a source reports a signed error (e.g. −2%) they are reporting the relative error or signed deviation, not the standard percent error.

What is the difference between percent error and percent difference?

Percent error compares a single measurement to a known reference (accepted) value — the denominator is the accepted value. Percent difference compares two measurements with no reference — the denominator is the average of the two values. Use percent error when you have a "correct" answer to compare against; use percent difference when both values carry equal uncertainty.

What counts as a good percent error in a lab?

It depends on the experiment and the field. In many high-school and undergraduate physics labs, under 5% is considered acceptable. Analytical chemistry often demands under 1%. Engineering safety-critical measurements may require under 0.1%. Always check the tolerance specified for your experiment.

What does the solve-for-variable mode do?

The two extra modes rearrange the percent error formula for a different unknown. "Find experimental value" gives the two measurement values (one over-estimate, one under-estimate) that would produce a specified percent error against a known accepted value. "Find accepted value" gives the reference value that would make your experimental reading correspond to a given percent error.

Percent Error Calculator

Percent error is the single most common way scientists and engineers quantify how close a measured result is to a known reference. Whether you are checking a lab thermometer against a calibrated standard, comparing a calculated gravitational constant against the textbook value, or auditing a sensor reading against a datasheet specification, percent error puts the discrepancy into an immediately meaningful scale.

This calculator handles all three cases in one place: the standard forward calculation (experimental + accepted → percent error), and two solve-for-variable modes that let you work backwards when you already know the percent error target.

The formula

The standard definition is:

Percent Error = (|Experimental − Accepted| / |Accepted|) × 100

where:

Experimental is the value you measured, calculated, or recorded.
Accepted (also called the true, theoretical, or reference value) is the known-correct value you are comparing against.
The vertical bars denote an absolute value, ensuring the result is always positive.

The result is expressed as a percentage of the accepted value, so it is a relative error — it automatically scales whether you are measuring centimetres or kilometres.

What the diagram shows

In the default mode the calculator draws a small SVG number line with a green tick for the accepted value, a blue tick for the experimental value, and a shaded span covering the gap between them. The percent-error label sits inside the span (when wide enough to fit). This visual makes it immediately obvious how large the error is relative to the scale of the measurement.

Worked example

Problem: A student measures the acceleration due to gravity and obtains 9.74 m/s². The accepted value is 9.81 m/s². What is the percent error?

Step 1 — absolute error: |9.74 − 9.81| = 0.07 m/s²

Step 2 — divide by the accepted value: 0.07 / 9.81 = 0.00714…

Step 3 — convert to percentage: 0.00714 × 100 = 0.71%

The experimental reading is 0.71% below the accepted value — a very respectable result for a school experiment.

Solve-for-variable example

Suppose the student knows that the equipment tolerance means the result must fall within 2% of the accepted value of 9.81 m/s², and wants to know the allowable measurement range.

Switch the dropdown to “Find experimental value”, enter 9.81 as the accepted value and 2 as the percent error. The calculator returns:

Over-estimate: 9.81 + 9.81 × 0.02 = 10.0062 m/s²
Under-estimate: 9.81 − 9.81 × 0.02 = 9.6138 m/s²

Any reading between 9.6138 and 10.0062 m/s² is within the 2% tolerance.

Quick reference table

Experimental	Accepted	Percent error
9.74 m/s²	9.81 m/s²	0.71%
98.5 g	100.0 g	1.50%
2.95 × 10^8 m/s	3.00 × 10^8 m/s	1.67%
4.12 V	4.00 V	3.00%

Formula note

When the accepted value is zero the formula is undefined (division by zero). In that case, some textbooks substitute a small positive reference or use the absolute error alone. This calculator flags the condition rather than silently returning infinity.

For the solve-for-variable modes the formula is simply rearranged:

Find experimental: Experimental = Accepted ± |Accepted| × (PE / 100)
Find accepted (over branch): |Accepted| = |Experimental| / (1 + PE / 100)
Find accepted (under branch): |Accepted| = |Experimental| / (1 − PE / 100)

Because the original formula has an absolute value, each inverse problem has two symmetric solutions — the calculator shows both.

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