Percentage Difference vs. Percentage Change
Percentage Difference (Symmetric)
Formula: |V₁ − V₂| / ((V₁ + V₂) / 2) × 100. This gives a symmetric result — the percentage difference between 50 and 75 is the same as between 75 and 50 (40%). Used when neither value is clearly the 'original.'
Percentage Change (Directional)
Formula: (New − Old) / Old × 100. This is directional — going from 50 to 75 is +50%, but going from 75 to 50 is −33.3%. Used when you have a clear before/after or old/new relationship.
| Calculation | Formula | Example: 80 to 100 |
|---|---|---|
| % Difference | |V₁−V₂|/avg×100 | 22.2% |
| % Change | (New−Old)/Old×100 | +25.0% |
| % Increase | (New−Old)/Old×100 | +25.0% |
Common Percentage Calculations
What is X% of Y?
Formula: Y × (X / 100). Example: 15% of $85 = $85 × 0.15 = $12.75. This is the most common percentage calculation — used for tips, discounts, and tax.
X is What % of Y?
Formula: (X / Y) × 100. Example: 30 is what % of 120? → (30/120) × 100 = 25%.
Percentage Increase/Decrease
To increase a number by X%: multiply by (1 + X/100). To decrease by X%: multiply by (1 − X/100). A 20% increase on $50: $50 × 1.20 = $60. A 20% decrease on $50: $50 × 0.80 = $40. Note: a 20% increase followed by a 20% decrease does NOT return to the original — $60 × 0.80 = $48, not $50.
Step-by-Step Instructions
- 1Select the calculation mode.
- 2Enter the two values you want to compare.
- 3View the result with step-by-step formula breakdown.
- 4Copy the result or try a different calculation mode.