Percent Error Calculator
Calculate the percent error between your experimental measurement and the accepted theoretical value. Used in physics, chemistry, and all scientific experiments.
How to Use
- Enter the experimental value: The measurement you obtained in your lab or experiment.
- Enter the theoretical value: The accepted, known, or expected value (from a textbook, standard, or reference).
- Read the results: The percent error, absolute error, signed error, and direction (too high or too low) appear instantly.
- Include units consistently — both values must be in the same unit for meaningful results.
What You'll Discover
- Percent error — how far your measurement is from the accepted value, as a percentage of the accepted value. This is the number most lab reports ask for.
- Absolute error — the raw size of the gap, |E − T|, in the same units as your measurement.
- Signed error — E − T with its sign kept, so you can see whether you overshot (+) or undershot (−).
- Direction — a plain-language label (too high, too low, or exact match) that helps you spot systematic bias across repeated trials.
If the theoretical value is zero, percent error is undefined because you would be dividing by zero. The calculator still shows the absolute and signed error so you can report those instead.
Formula
The standard percent error formula uses the absolute value of the difference, expressed as a percentage of the theoretical value:
% Error = |E − T| / |T| × 100%
Where E is the experimental value and T is the theoretical (accepted) value. The absolute value bars (| |) make the result always positive, representing the magnitude of error regardless of direction.
Absolute Error
Absolute error = |E − T|
Signed Error (with direction)
The signed error tells you whether your measurement was too high or too low:
Signed error = E − T
A positive signed error means your experimental value was too high; a negative value means it was too low.
Examples
Example 1 — Gravitational acceleration
You measure acceleration due to gravity as 9.8 m/s². The accepted value is 9.81 m/s².
- Absolute error: |9.8 − 9.81| = 0.01 m/s²
- % Error: 0.01 / 9.81 × 100 ≈ 0.102% — excellent accuracy
- Direction: too low (measured less than accepted)
Example 2 — Density experiment
A student measures the density of water as 0.97 g/cm³. The accepted value is 1.00 g/cm³.
- Absolute error: |0.97 − 1.00| = 0.03
- % Error: 0.03 / 1.00 × 100 = 3%
- Direction: too low (temperature or impurities likely caused the deviation)
Example 3 — Resistor measurement
An ohmmeter reads 105 Ω for a resistor rated at 100 Ω.
- Absolute error: |105 − 100| = 5 Ω
- % Error: 5 / 100 × 100 = 5% — within typical resistor tolerance
- Direction: too high
Percent Error vs Percent Difference vs Percent Change
These three formulas look alike, and students often mix them up. The difference is what you divide by, which depends on whether one of your two numbers is the "correct" one.
| Measure | Formula | Use it when |
|---|---|---|
| Percent error | |E − T| / |T| × 100 | You are comparing a measurement against a known, accepted value. |
| Percent difference | |A − B| / ((A + B) / 2) × 100 | You are comparing two measurements and neither is the "true" value. |
| Percent change | (New − Old) / |Old| × 100 | A value moved over time and you want the size and direction of the move. |
Because percent error divides by the accepted value, swapping the two inputs changes the answer. A reading of 105 against an accepted 100 is a 5% error, but a reading of 100 against an accepted 105 is about 4.76%. Always put the reference value in the theoretical field.
Accuracy vs precision
Percent error measures accuracy: how close a result is to the true value. It says nothing about precision, which is how close repeated measurements are to each other. Five readings of 9.50, 9.51, 9.50, 9.49 and 9.50 m/s² are very precise, yet each has about a 3.2% error against 9.81 m/s². A tight cluster with a large error usually points to a systematic problem, such as a miscalibrated instrument, rather than random noise.
Relative error and percent error
Relative error is the same ratio without the × 100: |E − T| / |T|. A relative error of 0.025 is a percent error of 2.5%. Engineering and numerical-methods texts often quote relative error; chemistry and physics lab manuals usually ask for percent error.
What Is My Percent Error If...
What is my percent error if I measured g as 9.7 m/s²?
Measuring 9.7 m/s² against the accepted 9.81 m/s² gives a percent error of about 1.12%. The absolute error is 0.11 m/s², and 0.11 ÷ 9.81 × 100 ≈ 1.12%. Your result is too low, which is common in pendulum experiments that ignore air resistance or measure the string length to the wrong point on the bob.
What is my percent error if water boiled at 98.5 °C instead of 100 °C?
A boiling point of 98.5 °C against 100 °C is a 1.5% error. The gap is 1.5 °C, and 1.5 ÷ 100 × 100 = 1.5%. This may not be a mistake at all: water boils below 100 °C at altitude, so check whether the accepted value should be adjusted for your local air pressure.
What is my percent error if I got 52 and the answer is 50?
A result of 52 against an accepted 50 is a 4% error, too high. The absolute error is 2, and 2 ÷ 50 × 100 = 4%. Getting 48 instead would also be a 4% error, but too low. The unsigned percent error is the same; only the signed error shows the direction.
What is my percent error if I measured aluminium's density as 2.85 g/cm³?
Against the accepted 2.70 g/cm³, a reading of 2.85 g/cm³ is about a 5.56% error. The absolute error is 0.15 g/cm³, and 0.15 ÷ 2.70 × 100 ≈ 5.56%. A high density reading often means the volume was underestimated, for example by reading the water displacement from the top of the meniscus instead of the bottom.
What is my percent error if I measured the speed of sound as 330 m/s?
Against 343 m/s (dry air at 20 °C), 330 m/s is about a 3.79% error. The gap is 13 m/s, and 13 ÷ 343 × 100 ≈ 3.79%. The speed of sound rises by roughly 0.6 m/s per °C, so a cold room alone can explain part of a low reading.
What is my percent error if my measurement is exactly twice the accepted value?
A measurement double the accepted value is a 100% error. If T = 25 and E = 50, the error is 25, and 25 ÷ 25 × 100 = 100%. Errors this large almost always come from a unit mix-up (grams vs kilograms, cm vs m) or a missing factor of two in the formula, not from measurement noise.
What is my percent error if my percent yield was 85%?
A percent yield of 85% corresponds to a 15% error relative to the theoretical yield. Percent yield is actual ÷ theoretical × 100. When the actual yield is below the theoretical, percent error equals 100% minus the percent yield. Enter the actual mass as the experimental value and the theoretical mass as the theoretical value to see the same 15%.
What is my percent error if the accepted value is negative?
Percent error uses the absolute value of the accepted value, so a measured −5.2 against an accepted −5.0 is a 4% error. The absolute error is |−5.2 − (−5.0)| = 0.2, and 0.2 ÷ |−5.0| × 100 = 4%. The signed error is −0.2, meaning the measurement was further below zero than the accepted value.
What is my percent error if the accepted value is zero?
Percent error is undefined when the accepted value is zero, because the formula divides by zero. In this case, report the absolute error instead (for example, "the reading was 0.03 V off a true zero"). The calculator shows the absolute and signed error even when T = 0.
What is my percent error if my measurement matches exactly?
If your measurement equals the accepted value, the percent error is 0%. In practice an exact match usually reflects rounding: both numbers agree to the number of significant figures you recorded. It is still worth noting the precision of your instrument in your report.
People Also Search For
How to calculate percent error by hand
Subtract the accepted value from your measured value, drop any minus sign, divide by the accepted value, and multiply by 100. For a measured 9.8 and an accepted 9.81: 9.8 − 9.81 = −0.01, the absolute value is 0.01, 0.01 ÷ 9.81 = 0.00102, and × 100 gives about 0.102%. Keep the full value until the last step and round only the final answer.
Percent error vs percent difference
Use percent error when one value is known to be correct; use percent difference when comparing two measurements of equal standing. Percent difference divides by the average of the two values instead of an accepted value. For 9.8 and 9.81 the percent difference is 0.01 ÷ 9.805 × 100 ≈ 0.102%, nearly identical here, but the two diverge as the values move further apart.
How to calculate percent yield and its error
Percent yield is actual yield ÷ theoretical yield × 100, and its percent error is |actual − theoretical| ÷ theoretical × 100. If you made 4.2 g of product with a theoretical yield of 5.0 g, the percent yield is 84% and the percent error is 16%. Enter 4.2 and 5.0 into the calculator above to check.
What is relative error
Relative error is the absolute error divided by the size of the true value: |E − T| ÷ |T|. It is a unitless ratio, so you can compare the accuracy of measurements made in different units. Multiply it by 100 to get percent error, or by 1,000 for parts per thousand.
Can percent error be negative
The standard percent error is never negative because it uses absolute value, but the signed version can be. Some teachers ask for (E − T) ÷ T × 100 without the absolute value so the sign shows whether you were high or low. The calculator gives you both: percent error as the headline and the signed error with its direction below it.
How to reduce percent error in a lab experiment
Calibrate instruments, take repeated readings and average them, and control the conditions that affect your result. Averaging reduces random error. It will not fix systematic error, so also check zero offsets, read scales at eye level to avoid parallax, and record temperature and pressure when the accepted value depends on them.
Frequently Asked Questions
What is a good percent error?
It depends on the field and purpose. In most high school and undergraduate labs, less than 5% is considered acceptable. In analytical chemistry or precision measurement, errors of less than 1% may be required. In industrial manufacturing, error tolerances depend on the specification. Always compare your percent error against the stated precision requirements of your experiment or standard.
What is the difference between signed and unsigned percent error?
Unsigned (absolute) percent error uses |E − T| and is always positive — it only tells you the magnitude of the error. Signed percent error (without absolute value) can be positive or negative: positive means you measured too high, negative means too low. Scientists usually report unsigned percent error as the standard metric but also report signed error when the direction of bias matters.
Why is percent error calculated relative to the theoretical value (not the experimental one)?
The theoretical value is the reference standard — it represents truth or the best-known correct answer. Calculating relative to it gives a meaningful scale: a 1-unit error on a measurement of 100 is very different from a 1-unit error on a measurement of 2. Using the theoretical value as the denominator allows fair comparison of accuracy across different scales and units.
What causes percent error in experiments?
Common sources include: instrument limitations (limited precision or calibration drift), human error (parallax, reading errors), environmental factors (temperature, humidity, vibration), systematic errors (a consistently biased measurement method), and random errors (statistical fluctuations). Understanding the source helps you identify improvements for future measurements.
Can percent error be greater than 100%?
Yes. If your experimental value is more than twice the theoretical value (or less than zero for a positive theoretical), the percent error exceeds 100%. This typically signals a significant problem — a wrong unit conversion, a missing factor in the setup, or a recording error. A percent error above 100% should prompt a review of the experimental procedure rather than just the data.
Does the order of the two values matter?
Yes. Percent error divides by the theoretical value, so swapping the inputs changes the result. A measured 105 against an accepted 100 is a 5% error, while a measured 100 against an accepted 105 is about 4.76%. Always enter the accepted or reference value in the theoretical field.
Is percent error the same as percent change?
No. Percent change compares a new value with an old one and keeps its sign, so it can show growth or decline. Percent error compares a measurement with an accepted value and is normally reported as a positive magnitude. The arithmetic is similar, but the reference value and the meaning are different.
What happens if the theoretical value is zero?
Percent error is undefined when the theoretical value is zero, because the formula would divide by zero. The calculator flags this and still shows the absolute and signed error, which you can report instead.
How many decimal places should I report?
Match the precision of your data. A common rule is to report percent error to two or three significant figures, for example 1.12% rather than 1.1213%. More digits than your measurements support suggest false precision. Check your course or lab manual, as some specify a format.
Can I use this calculator for percent yield?
Yes, for the error part. Enter your actual yield as the experimental value and the theoretical yield as the theoretical value. The percent error shown is how far your yield fell short of (or exceeded) the theoretical amount. Percent yield itself is actual ÷ theoretical × 100.
What if there is no accepted value to compare against?
Percent error needs a reference value, so it does not apply. If you are comparing two of your own measurements, use percent difference, which divides by their average. If you have many repeated readings, describe their spread with the standard deviation instead.
Is percent error the same as margin of error or standard error?
No. Percent error compares one result with a known true value. Margin of error and standard error are statistical measures of uncertainty that come from the spread of repeated measurements or a sample; they do not need a known true value. A lab report may include both: percent error for accuracy and standard error for the uncertainty of the mean.
Is my data stored or sent anywhere?
No. All calculations run in your browser. Nothing you type is sent to a server or saved, and no account is needed.
Last reviewed: November 2026 — formulas and worked examples verified.