Calculate percent error between a measured or experimental value and an actual, accepted, or theoretical value. See absolute error, relative error, signed direction, formulas, substituted numbers, and step-by-step math.
Enter a measured value and an actual/accepted value to see the full error breakdown.
Decimals, negative numbers, and simple fractions such as 49/10 are all accepted. Percent error itself is unitless; a unit here only labels the absolute and signed error.
Percent error measures how far a measured, observed, or experimental value is from an accepted, actual, theoretical, or reference value, relative to the size of that reference value. The result is expressed as a percentage. Suppose an accepted value is 50 and an experiment produces 48.5. The difference is 48.5 - 50 = -1.5. The negative sign tells us that the measured value is below the reference value. For standard percent error, however, we use the absolute size of the error: |-1.5| = 1.5. Then divide by the magnitude of the accepted value: 1.5 / 50 = 0.03. Convert the decimal to a percentage: 0.03 x 100 = 3%. Therefore the percent error is 3%.
Percent error is especially useful when the same numerical error could mean very different things at different scales. An error of 2 units may be tiny when the reference value is 1,000, but enormous when the reference value is 5.
The standard percent error formula is Percent Error = |Measured - Actual| / |Actual| x 100%. Using symbols, Percent Error = |M - A| / |A| x 100%, where M is the measured or experimental value and A is the actual, accepted, theoretical, or reference value. The vertical bars, | |, mean absolute value. Absolute value removes the positive or negative direction and keeps only the size of the difference. For example, |-3| = 3, and |3| = 3. That is why standard percent error is normally reported as a nonnegative percentage.
Use the values Measured: 48.5 and Actual: 50. Step 1: subtract the actual value from the measured value: 48.5 - 50 = -1.5. Step 2: take the absolute value: |-1.5| = 1.5. Step 3: divide by the magnitude of the actual value: 1.5 / 50 = 0.03. Step 4: multiply by 100: 0.03 x 100 = 3. Step 5: add the percent sign: Percent Error = 3%. The measured value was below the actual value, but the standard percent error itself is positive 3%.
Without absolute value, a measured value below the accepted value would produce a negative difference. Example: Measured 90, Actual 100. Difference: 90 - 100 = -10. But the size of the measurement error is 10. Standard percent error focuses on the magnitude of the discrepancy. Therefore |-10| = 10, and Percent Error = 10 / 100 x 100 = 10%. The negative direction can still be useful, but it should be reported separately. That is why this calculator also shows whether the measured value was above or below the accepted value.
Signed error keeps the direction of the difference. Formula: Signed Error = Measured - Actual. Example: Measured 90, Actual 100, Signed Error = -10. Interpretation: the measured value is 10 units below the accepted value. If Measured is 110 and Actual is 100, Signed Error = +10, meaning the measured value is 10 units above the accepted value. Signed error and standard percent error answer related but different questions.
Absolute error is the size of the difference between the measured and accepted values. Formula: Absolute Error = |Measured - Actual|. Example: Measured 19.7 cm, Actual 20 cm. Absolute Error = |19.7 - 20| = 0.3 cm. Unlike percent error, absolute error retains the original measurement units. In this example, the absolute error is 0.3 cm.
Relative error compares the absolute error with the magnitude of the reference value. Formula: Relative Error = Absolute Error / |Actual Value|. Example: Absolute Error 1.5, Actual 50, Relative Error = 1.5 / 50 = 0.03. Relative error is usually written as a decimal. Percent error expresses the same relationship as a percentage: 0.03 x 100 = 3%. So Relative Error = 0.03 and Percent Error = 3%.
Absolute error alone does not tell you whether an error is large relative to the quantity being measured. Consider two situations. Case A: Actual 100, Measured 98, Absolute Error 2, Percent Error 2%. Case B: Actual 10, Measured 8, Absolute Error 2, Percent Error 20%. Both measurements miss the reference value by 2 units. But 2 units is a much larger portion of 10 than of 100. Percent error captures that scale difference.
A lower percent error means the measured value is relatively closer to the provided reference value. Example: Measured 99, Actual 100, Percent Error 1%. That is closer to the reference value than Measured 90, Actual 100, Percent Error 10%. However, a low percent error does not automatically prove that an experiment, measurement method, instrument, or conclusion is scientifically valid. Percent error tells you how close the entered measured value is to the entered reference value. Other forms of uncertainty and experimental quality may still matter.
A higher percent error means the measured value is farther from the reference value relative to the size of that reference. Example: Measured 75, Actual 100, Absolute Error 25, Percent Error 25%. Whether 25% is acceptable depends completely on the context. There is no universal acceptable percent-error threshold.
There is no single percentage that is automatically acceptable in every situation. Acceptable error depends on factors such as the measurement method, the instrument, the experiment, the industry, the required tolerance, the assignment instructions, the scientific standard, the safety consequences, and the purpose of the result. A classroom demonstration may tolerate more error than precision manufacturing, medical equipment, or calibration work. Always compare the calculated percent error with the tolerance or expectation that actually applies to your situation. Do not use a generic rule such as "under 5% is always good." That is not universally valid.
This is one of the most important limitations of the percent-error formula. Suppose Actual Value: 0. The formula requires Absolute Error / |Actual|. That would require division by 0. Division by zero is undefined. Therefore standard percent error cannot be calculated when the accepted or reference value is 0. Example: Measured 2, Actual 0, Absolute Error 2, but Percent Error: Undefined. The calculator should still show the absolute difference while explaining why no relative or percent error exists.
Suppose Measured: 0, Actual: 0. The absolute difference is 0. But relative error would require 0/0, and that expression does not define a unique percentage. Therefore standard percent error remains undefined. Do not automatically report 0%.
Standard percent error using |Measured - Actual| / |Actual| x 100% is not negative. The absolute value removes the sign of the difference. If you want to know direction, use a separate signed calculation. Example: Measured 48.5, Actual 50, Standard Percent Error 3%, Signed Relative Error -3%. The negative signed result tells us the measured value is below the reference value. It should not replace the standard percent-error result.
Yes. Example: Measured 25, Actual 10. Absolute Error = |25 - 10| = 15. Percent Error = 15 / 10 x 100 = 150%. A percent error greater than 100% means the size of the error is greater than the magnitude of the reference value. It is mathematically possible.
Yes. Example: Measured 25, Actual 25, Absolute Error 0, Percent Error 0%. The two entered values match exactly. That means there is no difference relative to the supplied reference value. It does not automatically prove that the reference value itself is universally correct.
Percent error can still be calculated when the reference value is negative, as long as the reference is not 0. Example: Measured -9, Actual -10. Difference: -9 - (-10) = 1. Absolute Error = 1. Magnitude of Actual: |-10| = 10. Percent Error = 1 / 10 x 100 = 10%. Using the magnitude of the denominator prevents an ordinary magnitude-based error percentage from becoming negative simply because the reference value is negative.
Percent error is most appropriate when one value is treated as the actual, accepted, theoretical, or reference value. Percent difference is commonly used when comparing two values where neither is necessarily the one accepted true value. A common percent-difference formula is |A - B| / ((|A| + |B|) / 2) x 100%. Example: Experimental Result 1 is 48, Experimental Result 2 is 52. Neither may be designated as the accepted value. In that situation percent difference may be the more appropriate comparison. Do not confuse the denominator used in percent difference with the denominator used in percent error.
Percent change measures movement from an original value to a new value. Example: a price changes from $50 to $60, a percent change of 20% increase. Percent error asks a different question: how far is a measured value from a reference or accepted value? If you have an original value and a new value and need the percent increase or decrease, the Percentage Change Calculator handles that calculation directly. Do not merge the two calculators.
General percentage problems may ask "What is 30% of 200?" or "What percent is 15 of 60?" Those are not necessarily error calculations. Use the Percentage Calculator for general percentage questions. Use this page when you have a measured or experimental value and an accepted or reference value.
Percent error compares one measured result, or sometimes an average result, against a reference value. Standard deviation measures how spread out multiple observations are around their mean. Example: suppose repeated measurements are 9.7, 9.8, 10.1, 10.2, and 10.2. Standard deviation helps describe how tightly those repeated measurements cluster. Percent error can compare their mean to a known accepted value. These measures answer different questions. Use the Standard Deviation Calculator for spread calculations.
Percent error and margin of error are not the same. Percent error compares a measured or observed result with a reference value. Margin of error is commonly associated with estimates from samples and indicates a range of uncertainty around an estimate. For example, polling, surveys, sample proportions, and confidence intervals may use margin-of-error concepts. Do not use this Percent Error Calculator as a margin-of-error calculator. If you need descriptive statistics such as mean, median, quartiles, IQR, or range, the Statistics Calculator covers those calculations separately.
Percent error appears often in laboratory work when an experimental result can be compared with an accepted or theoretical value. Suppose a physics experiment measures gravitational acceleration as 9.72 m/s². An accepted reference used for the problem is 9.81 m/s². Absolute Error = |9.72 - 9.81| = 0.09 m/s². Percent Error = 0.09 / 9.81 x 100 ≈ 0.917%. This tells you how far the experimental value is from the supplied reference value relative to the size of that reference.
Chemistry experiments may compare experimental mass, density, melting point, volume, reaction result, or another measured property with an accepted or theoretical value. Example: Measured density 7.70 g/cm³, Accepted density 7.87 g/cm³. Absolute Error = 0.17 g/cm³. Percent Error = 0.17 / 7.87 x 100 ≈ 2.16%. The percent-error calculation does not explain why the values differ. Possible causes might involve measurement limitations, sample conditions, procedure, instrument precision, or other experimental factors. Those causes require scientific interpretation beyond the arithmetic itself.
For readers who learn better by watching a worked example, the site owner supplied a YouTube percent error lesson. You can watch a visual percent error example as optional supplementary learning. No transcript, examples, graphics, wording, or teaching sequence from that video have been copied onto this page.
Use this process. Step 1: identify the measured or experimental result. Step 2: identify the accepted, actual, theoretical, or reference value. Step 3: subtract, Measured - Actual. Step 4: take the absolute value of the difference. Step 5: divide by the magnitude of the actual or reference value. Step 6: multiply by 100. Step 7: add the percent sign. Step 8: separately note whether the measured value was above or below the reference value if that direction matters.
Do not round too early. Keep extra precision during the calculation and round the final displayed percent error. Example: 0.09 / 9.81 x 100 = 0.917431... If the answer needs 3 decimal places, report 0.917%. If the assignment requests 2 significant figures, report 0.92%. Use the Rounding Calculator for detailed rounding rules, including decimal places, significant figures, and rounding methods.
For the standard percent-error formula used on this page, use the actual, accepted, or reference value in the denominator. Formula: |Measured - Actual| / |Actual| x 100%. Using the measured value in the denominator creates a different relative comparison. The denominator must match the definition of the quantity being calculated.
Forgetting the absolute value. Standard percent error should not become negative simply because the measured value is below the reference.
Dividing by the measured value. For this standard percent-error formula, divide by the magnitude of the accepted or reference value.
Forgetting to multiply by 100. Relative error 0.03 is percent error 3%.
Confusing percent error with percent change. They answer different questions.
Confusing percent error with percent difference. Percent difference commonly uses an average in the denominator when neither value is treated as the accepted reference.
Calling signed error "percent error." Direction should be shown separately.
Calculating percent error when the reference value is zero. Standard percent error is undefined when the denominator is 0.
Rounding too early. Keep extra digits during intermediate steps.
Assuming a certain percent error is always acceptable. Tolerance is context-specific.
Do not leave knowing only "my percent error is 3%." Leave knowing what percent error measures, and the difference between a measured value and a reference value. Know the percent error formula, and understand why absolute value is used. Know that standard percent error is normally nonnegative, and understand signed error, absolute error, and relative error. Know how to identify whether your measurement was above or below the reference value, and know why the reference value belongs in the denominator. Understand what happens if the reference value is zero, and know percent error can exceed 100%. Understand that 0% error means the entered values match, and know the difference between percent error and percent difference, percent error and percent change, and percent error and margin of error. Understand that standard deviation measures something different, and know there is no universal acceptable percent-error threshold. Understand how percent error appears in science and experiments, and know not to round too early. Most importantly, you can see why the Percent Error Calculator produced the answer it did. That is what the CalculateThisWay Percent Error Calculator should help someone understand.
| Concept | Formula |
|---|---|
| Signed Error | Measured - Actual |
| Absolute Error | |Measured - Actual| |
| Relative Error | |Measured - Actual| / |Actual| |
| Percent Error | |Measured - Actual| / |Actual| × 100% |
| Signed Relative Error | (Measured - Actual) / |Actual| × 100% |
| Measured Above Actual | Signed Error > 0 |
| Measured Below Actual | Signed Error < 0 |
| Exact Match | Signed Error = 0 |
| Percent Error With Actual = 0 | Undefined |
I have a measured or experimental value and an accepted/reference value and need to know how far apart they are relative to the reference.
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Open Calculator ›I have an original value and a new value and need the percent increase or decrease.
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Open Calculator ›What is percent error?
Percent error measures how far a measured or experimental value is from an actual, accepted, or theoretical value, relative to the size of that reference value, expressed as a percentage. It is calculated as the absolute value of the difference divided by the absolute value of the actual value, times 100.
What is a percent error?
A percent error is the result of comparing one measured value with one accepted or reference value using the formula |Measured - Actual| / |Actual| × 100%. It tells you how big the gap is relative to the reference value.
What is the percent error formula?
The percent error formula is Percent Error = |Measured - Actual| / |Actual| × 100%, where Measured is the experimental value and Actual is the accepted, theoretical, or reference value.
How do you calculate percent error?
Subtract the actual value from the measured value, take the absolute value of that difference, divide by the absolute value of the actual value, then multiply by 100 to convert the decimal to a percentage.
How do I find percent error?
Find the absolute difference between your measured value and the actual value, divide that difference by the magnitude of the actual value, and multiply the result by 100.
How do you calculate percent of error?
Percent of error is another common phrasing for percent error, calculated the same way: |Measured - Actual| / |Actual| × 100%.
What is the error formula?
Depending on which error is meant, absolute error is |Measured - Actual|, signed error is Measured - Actual, relative error is |Measured - Actual| / |Actual|, and percent error is relative error expressed as a percentage.
What is the error percent formula?
The error percent formula is |Measured - Actual| / |Actual| × 100%, the same standard percent error formula used throughout this calculator.
What is absolute error?
Absolute error is the size of the difference between a measured value and an actual value, calculated as |Measured - Actual|. It is expressed in the same units as the original values and is never negative.
What is relative error?
Relative error compares the absolute error with the magnitude of the reference value: Relative Error = |Measured - Actual| / |Actual|. It is usually written as a decimal, such as 0.03.
What is signed error?
Signed error keeps the direction of the difference: Signed Error = Measured - Actual. A negative signed error means the measured value is below actual; a positive signed error means it is above actual.
What is signed relative error?
Signed relative error is (Measured - Actual) / |Actual| × 100%. Unlike standard percent error, it can be negative, and it is used only to show whether the measured value was above or below the reference.
Why is absolute value used in percent error?
Absolute value removes the positive or negative sign of the difference so that percent error reports the size of the measurement gap rather than its direction, which is reported separately as signed error or direction.
Can percent error be negative?
No. Standard percent error uses absolute value in both the numerator and denominator, so it is always zero or positive. Direction is reported separately through signed error, signed relative error, or a direction label.
Can percent error be greater than 100%?
Yes. If the size of the error is larger than the magnitude of the actual value, percent error exceeds 100%. For example, measured 25 versus actual 10 gives a percent error of 150%.
Can percent error be 0%?
Yes, when the measured value and the actual value are exactly equal, the absolute error is 0 and the percent error is 0%.
What does 0% percent error mean?
A 0% percent error means the entered measured value and actual value match exactly. It does not prove the reference value itself is universally correct.
What is a good percent error?
There is no single percent error that is automatically good in every situation. What counts as good depends on the instrument, the experiment, the industry, and the required tolerance.
What is an acceptable percent error?
There is no universal acceptable percent error. Acceptable error depends on the measurement method, instrument, experiment, industry standard, and the purpose of the result.
Is 5% percent error good?
It depends entirely on context. A 5% percent error might be fine for a classroom lab but unacceptable in precision manufacturing or medical calibration, so always compare against the tolerance that applies to your situation.
Why is there no universal acceptable percent error?
Because tolerance depends on factors such as the measurement instrument, the experiment, the industry, the assignment instructions, the scientific standard, and the safety consequences of the result, none of which are the same across every situation.
What happens if the actual value is zero?
Percent error and relative error become undefined because the formula requires dividing by the actual value, and division by zero has no defined result. Absolute error can still be reported.
What happens if both values are zero?
The absolute difference is 0, but percent error remains undefined because it would require calculating 0 divided by 0, which does not define a unique percentage. It should not be reported as 0%.
Can percent error use negative values?
Yes, as long as the actual value is not zero. The formula uses the absolute value of the actual value in the denominator, so a negative reference value is handled correctly.
Which value goes in the denominator?
The actual, accepted, theoretical, or reference value goes in the denominator, using its absolute value: |Measured - Actual| / |Actual| × 100%.
Do I divide by the measured value or actual value?
For standard percent error, divide by the absolute value of the actual or accepted value, not the measured value. Dividing by the measured value creates a different relative comparison.
What is the difference between percent error and absolute error?
Absolute error is the raw difference in original units, such as 2 cm. Percent error expresses that same difference relative to the actual value as a percentage, such as 2%.
What is the difference between percent error and relative error?
Relative error is usually written as a decimal, such as 0.03. Percent error is the same relationship expressed as a percentage, such as 3%.
What is the difference between percent error and percent difference?
Percent error compares a measured value with a designated actual or accepted value. Percent difference commonly compares two values where neither is treated as the single true reference, often using their average in the denominator.
What is the difference between percent error and percent change?
Percent change measures how a value moved from an original value to a new value. Percent error measures how far a measured value is from an accepted or reference value.
What is the difference between percent error and margin of error?
Percent error compares a measured or observed result with a reference value. Margin of error describes the uncertainty around an estimate, commonly used with samples, polling, and confidence intervals.
What is the difference between percent error and standard deviation?
Percent error compares one measured result, or an average result, with a reference value. Standard deviation describes how spread out a group of repeated measurements is around their own mean.
How is percent error used in chemistry?
Chemistry experiments often compare a measured mass, density, melting point, or volume with an accepted or theoretical value using the same percent error formula, such as comparing a measured density of 7.70 g/cm³ with an accepted 7.87 g/cm³.
How is percent error used in physics?
Physics labs often compare an experimental measurement, such as gravitational acceleration, with an accepted reference value, such as 9.81 m/s², using percent error to describe how close the experimental result came to the accepted value.
How do I round percent error?
Keep extra precision during the calculation and round only the final displayed percent error to the number of decimal places or significant figures your assignment or context requires.
Should I take absolute value before calculating percent error?
Yes. Take the absolute value of the difference between measured and actual, and use the absolute value of the actual value in the denominator, so the standard percent error result is never negative.
Standard percent error uses the magnitude of the difference between the measured and reference values: Percent Error = |Measured - Actual| / |Actual| × 100%. Signed error, Measured - Actual, is displayed separately from standard percent error so direction is never confused with the nonnegative percent-error result. Relative error is the absolute error divided by the magnitude of the reference value. Percent error and relative error are undefined when the reference value is zero, including when both entered values are zero, because that would require dividing by zero or evaluating 0/0; in that situation the absolute error can still be reported normally. Decimal results may be rounded for display while calculations retain greater internal precision, and unnecessary trailing zeros are removed from displayed percentages. Units you enter apply to signed error and absolute error, but cancel out in relative error and percent error since those are ratios. No universal percent-error threshold is assumed by this calculator; acceptable error always depends on the situation.
Last reviewed: September 28, 2026