Percentage Difference Calculator
Calculate the percentage difference between any two numbers. Shows the symmetric percentage difference, directional percentage change both ways, and absolute difference. Includes explanation of which value is larger and by how much.
Percentage Difference vs Percentage Change: Understanding the Crucial Difference
Many people confuse percentage difference with percentage change, but they are mathematically distinct concepts that answer different questions.
The Percentage Difference Formula
Also written as: % Difference = 2|V1 − V2| ÷ (V1 + V2) × 100
The formula uses the mean (average) of V1 and V2 as the denominator. This makes it symmetric: swapping V1 and V2 gives the same result. It is always positive (or zero if V1 = V2).
The Percentage Change Formula
Directional: positive = increase, negative = decrease
Worked Examples
Example 1: Comparing 40 and 60
- Absolute difference: |40 − 60| = 20
- Average: (40 + 60) ÷ 2 = 50
- Percentage difference: 20 ÷ 50 × 100 = 40%
- % change from 40 to 60: (60 − 40) ÷ 40 × 100 = +50%
- % change from 60 to 40: (40 − 60) ÷ 60 × 100 = −33.3%
Notice: the percentage difference is 40%, but the percentage changes (+50% and −33.3%) are different from each other and from the percentage difference.
Example 2: Scientific Measurement Comparison
Two students measure the boiling point of ethanol. Student A measures 77.8°C and Student B measures 79.2°C.
- |77.8 − 79.2| = 1.4
- Average: (77.8 + 79.2) ÷ 2 = 78.5
- % Difference = 1.4 ÷ 78.5 × 100 = 1.78%
A percentage difference of 1.78% suggests reasonable reproducibility for a student experiment. The actual boiling point of ethanol is 78.37°C — for this you would use percentage error (vs a known value), not percentage difference.
Example 3: Financial Analysis
A company’s sales this year are £250,000 and last year were £200,000.
- Percentage change (correct for growth measurement): (250,000 − 200,000) ÷ 200,000 × 100 = +25% growth
- Percentage difference: |250,000 − 200,000| ÷ ((250,000 + 200,000) ÷ 2) × 100 = 50,000 ÷ 225,000 × 100 = 22.2%
In this context, percentage change (+25%) is the correct metric because there is a clear direction (last year to this year). Use percentage difference when comparing two values without a defined before/after relationship.
When to Use Percentage Difference
Percentage difference is the right metric when:
- Comparing two experimental measurements with no clear baseline — e.g. two students measuring the same quantity
- Comparing prices at two shops where neither is the reference
- Comparing two estimates of the same unknown quantity
- Reporting survey results where you compare two subgroups without implying one caused the other
When to Use Percentage Change
Percentage change is correct when:
- Tracking change over time: price last month vs this month
- Before/after comparisons: weight before vs after a diet
- Growth rates: revenue this year vs last year
- UK exam questions on percentage change: GCSE Maths questions on percentage increase/decrease
Percentage Difference in UK GCSE Maths
GCSE Maths (Edexcel, AQA, OCR) does not typically test “percentage difference” by name — it focuses on percentage increase and percentage decrease, which are forms of percentage change. However, A-Level Statistics and university-level data analysis courses require understanding of symmetric measures like percentage difference.
| Metric | Formula | Direction? | Use Case |
|---|---|---|---|
| Percentage Difference | |V1−V2| ÷ avg × 100 | No (symmetric) | Comparing two measurements |
| Percentage Change | (New−Old) ÷ Old × 100 | Yes (+ or −) | Before/after, growth rates |
| Percentage Increase | (New−Old) ÷ Old × 100 (positive) | Yes (+) | GCSE increase questions |
| Percentage Decrease | (Old−New) ÷ Old × 100 (positive) | Yes (+) | GCSE decrease questions |
| Percentage Error | |Experimental−True| ÷ True × 100 | No | Science experiments |
The Asymmetry of Percentage Change
A common misconception is that a +50% increase followed by a −50% decrease returns you to the original value. It does not. If a price goes from £100 to £150 (+50%), then back down from £150 to £75 (−50%), the result is £75 — not £100. This asymmetry is why percentage difference (symmetric) is useful when you want to avoid implying direction or precedence.
Percentage Difference in Science and Research
In scientific literature, percentage difference appears when two independent measurements are compared. It is particularly common in:
- Physics lab reports: comparing two student measurements of the same constant
- Biology: comparing reaction rates under two conditions
- Economics: comparing regional price levels with no obvious baseline
- Medicine: comparing biomarker levels in two patient groups
- Quality control: comparing output from two production lines
Zero and Undefined Cases
If both values are zero, the percentage difference is zero (no difference). If one value is zero and the other is not, the formula gives a result of 200% (since the denominator is half of one value). In this special case, percentage change would be undefined (division by zero), making percentage difference the more robust choice.
Our calculator handles these edge cases automatically and flags any issues.
Frequently Asked Questions
What is percentage difference?
Percentage difference measures how much two values differ relative to their average. The formula is: % Difference = |V1 − V2| ÷ ((V1 + V2) ÷ 2) × 100. It is symmetric — the percentage difference between 10 and 20 is identical to that between 20 and 10 (both equal 66.7%). This makes it ideal when neither value is considered the baseline or reference point, such as comparing two lab measurements or two competing prices.
Is percentage difference the same as percentage change?
No, they are different. Percentage difference is symmetric and uses the average as the denominator — it has no direction. Percentage change is directional and uses the starting (original) value as the denominator. For 100 and 150: % difference = 40%; % change from 100 to 150 = +50%; % change from 150 to 100 = −33.3%. These three numbers are all different and cannot be used interchangeably.
How do I calculate percentage difference?
Four steps: (1) Find the absolute difference: |V1 − V2|. (2) Find the average: (V1 + V2) ÷ 2. (3) Divide the absolute difference by the average. (4) Multiply by 100 for a percentage. Example: V1=80, V2=100. Absolute difference = |80−100| = 20. Average = (80+100)÷2 = 90. % Difference = 20 ÷ 90 × 100 = 22.2%.
What is the formula for percentage difference?
The standard formula is: % Difference = |V1 − V2| ÷ ((V1 + V2) ÷ 2) × 100. This can also be written as 2|V1 − V2| ÷ (V1 + V2) × 100 (multiply numerator and denominator by 2). The key feature is that the denominator is the mean of the two values, ensuring symmetry. Some textbooks also write this as: % Difference = |V1 − V2| / mean(V1, V2) × 100.
Can percentage difference be negative?
No. Percentage difference, as defined with the absolute value |V1−V2|, is always zero or positive. It measures the magnitude of the difference without implying direction. The result is zero only when V1 and V2 are exactly equal. Percentage change, by contrast, can be negative (when the new value is smaller than the original). If you need a directional measure, use percentage change instead.
How is percentage difference used in science?
In science, percentage difference compares two experimental measurements when there is no single “true” reference value. For example: two students measure the density of copper and get 8.85 g/cm³ and 8.93 g/cm³. % Difference = |8.85−8.93| ÷ ((8.85+8.93)÷2) × 100 = 0.08 ÷ 8.89 × 100 = 0.90%. A small percentage difference indicates good reproducibility. When comparing against a known true value, use percentage error instead.