What is the percentage error if the true value is 50 and the measured value is 47?

|47 − 50| ÷ |50| × 100 = 3 ÷ 50 × 100 = 6%. The measurement is off by 6% relative to the true value. The signed error is (47 − 50) ÷ 50 × 100 = −6%, meaning the measurement was 6% below the true value (an underestimate).

% Change Guide

Percentage Error

Q: What is the formula for percentage error?

Percentage Error = |Measured Value − True Value| ÷ |True Value| × 100. The numerator is the absolute difference between your measurement and the accepted true value. The denominator is the absolute true value. For example, if you measure a mass as 48 g when the true mass is 50 g: |48 − 50| ÷ |50| × 100 = 2 ÷ 50 × 100 = 4% error.

Q: What is the difference between percentage error and percentage difference?

Percentage error requires one value to be the accepted true value — it measures how far off your measurement is from the truth, using the true value as the denominator. Percentage difference is symmetric — it compares two peer values with no designated truth, dividing by their average. Use percentage error when you know the correct answer; use percentage difference when comparing two equally valid measurements.

Q: What is a good percentage error?

It depends on the context and precision required. In a typical high school chemistry lab, errors under 5% are generally considered acceptable. Physics experiments often target under 2–3%. Engineering and manufacturing can require under 1% or even 0.1%. In everyday estimation — like estimating a crowd size or travel time — errors up to 10–20% may be perfectly reasonable. The standard is set by the discipline or instructor, not by a universal threshold.

Q: What is a signed vs unsigned percentage error?

The standard percentage error formula uses the absolute value |Measured − True|, making it always positive (unsigned). This tells you the magnitude of error. A signed version omits the absolute value bars: (Measured − True) ÷ |True| × 100. A positive signed error means you overestimated; a negative signed error means you underestimated. Signed error is useful when direction matters — like knowing whether a scale consistently reads high or low.

Q: Can percentage error be more than 100%?

Yes — if your measured value is more than double the true value, or if the true value is very small, percentage error can exceed 100%. For example, measuring 110 g when the true mass is 50 g: |110 − 50| ÷ 50 × 100 = 60 ÷ 50 × 100 = 120%. A percentage error over 100% means your measurement was off by more than the true value itself.

Q: What causes high percentage error in experiments?

High percentage error typically comes from parallax error (reading a scale at an angle), instrument calibration issues (a scale that hasn't been zeroed), rounding intermediate calculations, human reaction time in timing experiments, environmental factors (temperature, humidity), or systematic bias in the measurement method. Identifying whether the error is random or systematic helps determine how to reduce it in future trials.

Q: Why do you divide by the true value in percentage error?

The true value is the accepted standard — it's the reference against which accuracy is being measured. Dividing by it expresses the error as a proportion of what the value should have been. This makes percentage error comparable across experiments with different magnitudes: a 2 g error on a 50 g mass (4% error) is much more significant than a 2 g error on a 5000 g mass (0.04% error). Dividing by the true value captures that distinction.

The accuracy formula used in science, school labs, and engineering. Learn how to calculate how far off your measurement is from a known true value — with worked examples and common pitfalls.

Percentage Error = |Measured − True| ÷ |True| × 100

True Value is the accepted or theoretical value · result is always positive (unsigned)

How to Calculate Percentage Error

Percentage error tells you how accurate a measurement is. It compares your observed (measured) value to the accepted true value — expressed as a percentage of that true value. The smaller the percentage error, the closer your measurement is to the actual value. The formula always uses the true value as the denominator, because the true value is the standard against which accuracy is being judged.

Worked Example: Chemistry Lab Mass Measurement

A student measures the mass of a copper sample and gets 48.3 g. The accepted true mass is 50.0 g. What is the percentage error?

Step 1

Find the absolute difference (|Measured − True|)

|48.3 − 50.0| = 1.7 g. We use the absolute value — error is always expressed as a positive magnitude, not a direction.

Step 2

Divide by the absolute true value (|True|)

1.7 ÷ |50.0| = 0.034. The true value is the reference — we're measuring error as a fraction of how large the true value is.

Step 3

Multiply by 100 to convert to a percentage

0.034 × 100 = 3.4%. The measurement has a 3.4% error. In a typical high school lab, this would generally be considered acceptable.

Quick Reference: Common Scenarios

Scenario	Measured	True Value	Absolute Error	% Error
Mass measurement	48.3 g	50.0 g	1.7 g	3.4%
Length measurement	99 cm	100 cm	1 cm	1.0%
Temperature reading	102°C	100°C	2°C	2.0%
Volume measurement	47 mL	50 mL	3 mL	6.0%
Timing experiment	9.6 s	9.8 s	0.2 s	2.0%
Voltage reading	11.8 V	12.0 V	0.2 V	1.7%
Density experiment	8.6 g/cm³	8.96 g/cm³	0.36	4.0%

Signed vs Unsigned Percentage Error

The standard percentage error formula uses absolute value bars around the difference, making the result always positive. This is called the unsigned (or absolute) percentage error — it tells you the magnitude of the error without saying whether you measured too high or too low. Most textbooks and lab reports use unsigned error.

When Direction Matters: Signed Error

A signed percentage error omits the absolute value bars in the numerator: (Measured − True) ÷ |True| × 100. A positive signed error means you overestimated (measured too high). A negative signed error means you underestimated (measured too low).

Signed error is valuable when you need to diagnose systematic bias. If a balance consistently reads 2% high, the signed error reveals this pattern — whereas the unsigned error only tells you the measurements are off by 2%, not in which direction. Repeated signed errors in the same direction signal a calibration or methodology problem. Random errors — sometimes positive, sometimes negative — suggest random noise that can be reduced by averaging multiple trials.

Example: Signed Error in Both Directions

True value: 100 g. Measurement A: 104 g. Measurement B: 96 g.

Unsigned error: both are |4| ÷ 100 × 100 = 4% — they look identical in magnitude. Signed error tells the full story: Measurement A is +4% (overestimate), Measurement B is −4% (underestimate). If a student's scale consistently gives +4% signed error, the scale is reading high and needs recalibration. If measurements alternate between +4% and −4%, the variability is random and could be reduced through repeated measurement.

Acceptable Percentage Error by Discipline

Discipline	Typical Acceptable Error	Notes
High school chemistry	< 5%	General lab guideline; exact threshold varies by teacher
High school physics	< 3%	Timing and motion experiments often require tighter precision
Engineering	< 1% – 0.1%	Depends on application; structural engineering is tighter than estimates
Medical diagnostics	< 1%	Drug dosing and lab tests demand very high accuracy
Everyday estimation	< 10–20%	Crowd sizes, travel time, rough budgets
Manufacturing (tight tolerances)	< 0.01%	Aerospace, semiconductor fabrication

These are guidelines, not universal rules. The instructor or industry standard always takes precedence. Some experiments have inherent sources of error that make 5–10% unavoidable with basic equipment — in those cases, a higher percentage error may still earn full marks if the sources of error are correctly identified and discussed.

Percentage Error vs Percentage Difference

These two formulas are closely related but used in distinct situations. Understanding the difference prevents the most common error in lab reports and homework.

The Key Distinction: Do You Know the True Value?

Percentage error requires one value to be the accepted true or theoretical value. It measures the accuracy of a single measurement — how close you got to the "right" answer. The true value is always the denominator. This is the formula for science labs, quality control, and any situation where there is a correct answer to compare against.

Percentage difference treats both values as equally valid — there is no designated truth. It measures how much two peer measurements or quantities differ relative to their average. Use percentage difference when two researchers each take an independent measurement and neither is assumed to be "correct," or when comparing two stores' prices with no reference price.

When to Use Percentage Error vs Percentage Change

Percentage error and percentage change also get confused. Percentage change tracks how a value moved over time — from a starting point to a later value — and can be positive or negative. Percentage error is static: it compares a measurement to a fixed truth at a single point in time. A teacher marking your estimated answer as "8% off" from the correct answer is using percentage error. A stock that rose 8% from Monday to Friday is using percentage change.

Side-by-Side Formula Comparison

Formula	Numerator	Denominator	Symmetric?	Use When
% Error	\|Measured − True\|	\|True value\|	No	One value is the accepted truth
% Difference	\|V1 − V2\|	(V1 + V2) ÷ 2	Yes	Two peer values, no truth
% Change	New − Old	Old value	No	Before/after comparison over time
% Decrease	Old − New	Old value	No	Value went down over time

Common Sources of Error in Experiments

Understanding what drives percentage error in experiments helps you write better lab reports — and reduce errors in future trials. Sources of experimental error fall into two categories: systematic and random.

Systematic Errors

Systematic errors consistently push your results in one direction. They produce a consistent signed error and cannot be reduced by taking more measurements — only by fixing the root cause. Common examples include a scale that hasn't been zeroed (tare error), a ruler with a worn end that effectively adds length to every measurement, a thermometer that reads 2°C too high, or a stopwatch that starts a fraction of a second late every time. In these cases, your percentage error will be consistently positive or consistently negative across all trials. The fix is recalibration, not repetition.

Random Errors

Random errors scatter around the true value — sometimes high, sometimes low — with no predictable pattern. They arise from human reaction time variability, environmental fluctuations (air currents, vibration), reading a scale at slightly different angles, or the inherent resolution limit of the measuring instrument. Random errors show up as mixed positive and negative signed errors across trials. The remedy is to take multiple measurements and average them — random errors tend to cancel out across enough repetitions.

Parallax Error

Parallax error is one of the most common sources of measurement error in school labs. It occurs when you read a scale or graduated cylinder at an angle rather than straight on, causing you to read a value slightly above or below the true level. For liquid volumes, always read at eye level with the bottom of the meniscus. For analog meters, align your line of sight directly perpendicular to the scale.

Reducing Error in Your Lab Report

A good lab report doesn't just state the percentage error — it explains it. Identify whether the error appears systematic (consistent direction) or random (scattered). List the specific instruments used and their resolution limits, since even a perfect technique can't be more precise than the instrument allows. If your percentage error is high, propose concrete improvements: a more precise balance, a digital timer instead of a stopwatch, or a temperature-controlled environment. Listing "human error" without specifics is not an acceptable explanation in most science classes.

Percentage Error in Estimation and Everyday Life

Percentage error applies outside the lab too. If you estimate a 45-minute commute and it takes 52 minutes, your percentage error is |45 − 52| ÷ 52 × 100 = 13.5%. If a recipe calls for 200 g of flour and you measure 190 g, your percentage error is |190 − 200| ÷ 200 × 100 = 5%. Budget estimates, nutritional label accuracy, and construction measurements all involve percentage error — the formula is the same, even if the context is less formal than a chemistry lab. For financial comparisons where you're comparing two prices or values without a known truth, the percentage difference calculator is the appropriate tool instead.

Comparing two values without a true reference?

Use percentage difference — the symmetric formula for peer comparisons.

Percentage Difference →

Frequently Asked Questions

What is the formula for percentage error?

Percentage Error = |Measured Value − True Value| ÷ |True Value| × 100. The numerator is the absolute difference between your measurement and the accepted true value. For example, measuring 48 g when the true mass is 50 g: |48 − 50| ÷ |50| × 100 = 2 ÷ 50 × 100 = 4% error.

What is the difference between percentage error and percentage difference?

Percentage error requires one value to be the accepted true value — it measures how accurate a measurement is, using the true value as the denominator. Percentage difference is symmetric — it compares two peer values with no designated truth, using their average as the denominator. Use percentage error when you know the correct answer; use percentage difference when comparing two equally valid measurements.

What is a good percentage error?

It depends on the discipline. High school chemistry labs typically accept under 5%. Physics experiments often target under 3%. Engineering can require under 1% or 0.1%. Medical and pharmaceutical applications may demand under 0.5%. In everyday estimation (travel time, crowd size, budget), 10–20% may be perfectly reasonable. The threshold is always set by the instructor or industry standard, not a universal rule.

What is a signed vs unsigned percentage error?

The standard (unsigned) formula uses absolute value: |Measured − True| ÷ |True| × 100 — always positive, tells you the magnitude of the error. The signed version omits the absolute value in the numerator: (Measured − True) ÷ |True| × 100. A positive signed error means you overestimated; a negative signed error means you underestimated. Signed error is useful for detecting systematic bias in repeated measurements.

What is the percentage error if the true value is 50 and measured value is 47?

|47 − 50| ÷ |50| × 100 = 3 ÷ 50 × 100 = 6%. The measurement is 6% below the true value. The signed error is (47 − 50) ÷ 50 × 100 = −6%, confirming it's an underestimate — the measurement was too low.

Can percentage error be more than 100%?

Yes — if your measured value differs from the true value by more than the true value itself, percentage error exceeds 100%. Example: measuring 110 g when the true mass is 50 g: |110 − 50| ÷ 50 × 100 = 120%. A percentage error over 100% means the measurement was off by more than the true value — typically a sign of instrument failure, wrong units, or a fundamental methodological error.

What causes high percentage error in experiments?

High percentage error typically comes from: uncalibrated instruments (a scale not zeroed), parallax error (reading a scale at an angle), limited instrument resolution, human reaction time in timing experiments, environmental factors (temperature, vibration, air currents), or incorrect technique. Systematic causes produce consistent signed errors in one direction; random causes scatter the error. Identifying the type of error is as important as reporting the magnitude.

Why do you divide by the true value in percentage error?

The true value is the accepted standard — it's what the value should be. Dividing by it expresses error as a proportion of the "correct" answer. This makes percentage error comparable across experiments with different scales: a 2 g error on a 50 g mass (4% error) is far more significant than a 2 g error on a 5,000 g mass (0.04% error). Dividing by the true value captures that distinction and puts all experiments on an equal footing.