Percent difference formula (with plain-English meaning)

The percent difference formula compares how far apart two numbers are, relative to their average. The standard version (used in many math and science classes) is:

Percent difference (%) = |A − B| ÷ ((|A| + |B|) ÷ 2) × 100

• |A − B| is the absolute difference: how many units separate the two values (always positive).
• (|A| + |B|) ÷ 2 is the average magnitude: a fair “middle” value used as the reference.
• × 100 converts the ratio into a percent.

• Using the average makes the metric symmetric. Switching A and B doesn’t change the answer.
• It avoids the “which value is the baseline?” debate.
• It tends to be stable when A and B are close — perfect for measurement comparisons.

Step-by-step calculation (what the calculator does)

Here’s exactly how your percent difference is calculated. If you want to understand it once and never get confused again, read this section slowly one time — you’ll be set for life.

Subtract the two values and take the absolute value so the result is positive: |A − B|. If A = 120 and B = 100, the difference is 20.

Add the absolute values and divide by 2: (|A| + |B|) ÷ 2. For 120 and 100, the average is (120 + 100) ÷ 2 = 110.

Divide the difference by the average: 20 ÷ 110 = 0.181818… and multiply by 100 to get 18.18% (rounded).

• A = 0 and B = 0: both values are identical, so percent difference is 0%.
• Average = 0: happens only when both values are 0 (in absolute mode). We return 0%.
• Signed mode: if you choose “use signed values,” the average can be 0 when A = −B. In that case, percent difference is not defined (division by zero). The calculator will warn you.

Real-world examples you’ll actually use

Percent difference is everywhere — not just homework. Below are examples that feel “real,” so you can build intuition quickly. (And yes, these make great quick screenshots for social posts when you’re comparing numbers.)

Store A sells a product for $48. Store B sells it for $60. You’re not tracking “old vs new,” you’re comparing two offers. Difference = |48 − 60| = 12. Average = (48 + 60) ÷ 2 = 54. Percent difference = 12 ÷ 54 × 100 = 22.22%. Meaning: the prices are about 22% apart relative to the midpoint price.

Two devices measured the same sample: 9.8 and 10.3. Difference = 0.5. Average = (9.8 + 10.3) ÷ 2 = 10.05. Percent difference = 0.5 ÷ 10.05 × 100 = 4.98%. Meaning: the devices disagree by ~5% relative to the average reading.

You scored 86, the class average was 74. Difference = 12. Average = 80. Percent difference = 12 ÷ 80 × 100 = 15%. That’s a clean way to say your score was 15% away from the average (relative to the midpoint).

You walked 7,200 steps yesterday and 9,000 today. Difference = 1,800. Average = (7,200 + 9,000) ÷ 2 = 8,100. Percent difference = 1,800 ÷ 8,100 × 100 = 22.22%. If you post a progress screenshot, this number communicates “how different” the days were without calling yesterday the baseline.

If you bought something for $100 and it’s now $120, you have a clear baseline: $100. The best metric is percent increase = (120 − 100) ÷ 100 × 100 = 20%. Percent difference would give 18.18% (because it uses the average 110) — that’s not wrong mathematically, it’s just answering a different question.

Make your result more useful (and more shareable)

A percent by itself can be vague. The most “viral” comparisons include context, a one-line caption, and one extra number. Here’s how to make your percent difference result instantly understandable.

• Percent difference tells you the relative gap.
• Absolute difference tells you the real-world unit gap (dollars, points, steps, mg/dL, etc.).

• 0–1 decimals for quick social sharing (“about 22%”).
• 2–4 decimals for lab work, science classes, and careful reporting.

• For most comparisons, negatives just represent direction (profit/loss, temperature, elevation).
• Absolute mode compares magnitudes so the denominator stays meaningful.

• “These two prices are X% apart — which one would you choose?”
• “Same test, different result: X% difference. Should I retest?”
• “My steps today vs yesterday: X% gap. Accountability check.”
• “Two job offers. X% difference. Which is the better deal?”

Frequently Asked Questions

• What is percent difference?

  Percent difference measures how far apart two numbers are relative to their average. It’s commonly used when you’re comparing two values but you don’t have (or don’t want) a clear “original” baseline. It’s symmetric: swapping the two values doesn’t change the answer.

• How is percent difference different from percent change?

  Percent change uses a baseline (old) value: (new − old) ÷ old × 100. Percent difference uses the average of the two values: |A − B| ÷ ((|A| + |B|) ÷ 2) × 100. If you’re describing “before → after,” use percent change. If you’re comparing two independent values, use percent difference.

• Why does percent difference use the average in the denominator?

  The average makes the comparison fair and symmetric. If you used A as the denominator, you’d get a different answer than if you used B. The average provides a neutral midpoint reference.

• Is percent difference always positive?

  In the standard formula, yes. The absolute value |A − B| makes the numerator positive. Percent difference describes separation, not direction. If you need direction (increase vs decrease), use percent change instead.

• Can percent difference be over 100%?

  Yes. If one value is much larger than the other, the difference can exceed the average. Example: A = 1 and B = 9. Difference = 8. Average = 5. Percent difference = 8 ÷ 5 × 100 = 160%.

• What if one value is zero?

  It still works (in absolute mode). Example: A = 0 and B = 10 → difference 10, average 5 → percent difference 200%. If both are zero, percent difference is 0% because the values are identical.

• Should I use “absolute mode” or “signed mode”?

  For most real-world comparisons, absolute mode is safer because the denominator is based on magnitudes. Signed mode is mainly for special cases where sign carries meaning and you want the average to reflect direction. If signed mode creates a zero average (A = −B), percent difference becomes undefined.

• Is percent difference the same as percent error?

  No. Percent error compares a measured value to a “true” or accepted value: |measured − true| ÷ |true| × 100. Percent difference compares two measured values without choosing which is “true.”

• What’s a “good” percent difference?

  It depends on the context. In measurement, smaller percent difference can mean better agreement between instruments. In pricing, a larger percent difference can indicate a better deal if you’re choosing the cheaper option. The calculator is neutral — it reports the gap; you decide what that means.

• Does this calculator store my values?

  No. Calculations happen in your browser. If you press “Save Result,” it saves to local storage on your device only (so you can compare multiple pairs).