Percentage Increase Calculator Calculators

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Percentage increase measures how much a quantity has grown relative to its original value: % increase = (new value − old value) / old value × 100%. It is used widely in science, finance, epidemiology, and everyday life — from stock market changes to bacterial growth rates to clinical outcome comparisons. Percentage decrease uses the same formula with a negative result. Percentage change (more general) = (new − old) / |old| × 100%. To find the new value after a known percentage increase: new value = old value × (1 + % / 100). To reverse a percentage increase (find the original value): original = final / (1 + % / 100).

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Percentage Increase Formula

% increase = (new − old) / old × 100

Example: sales increased from 500 to 650: % increase = (650−500)/500 × 100 = 150/500 × 100 = 30%.

Applying a Percentage Increase

New value = old × (1 + rate/100). Example: price increases 15% from $80: new = 80 × 1.15 = $92.

Reversing a Percentage Increase

Original = final / (1 + rate/100). Example: after 20% increase, price is $120 — what was the original? Original = 120/1.20 = $100. (Common error: subtract 20% from $120 = $96 → wrong!)

Percentage Change vs. Percentage Points

Percentage change: relative change (% increase formula above). Percentage points (pp): absolute change in percentages. Example: interest rate rises from 5% to 7% = +2 percentage points but +40% percentage change (2/5 × 100). Both are correct — context determines which to report.

Glossary

Percentage Increase
(New − old) / old × 100; relative change from old to new value; negative = percentage decrease; new value = old × (1 + %/100).
Reverse Percentage
Finding the original value before a percentage increase: original = final / (1 + %/100); e.g., $138 after 15% increase → original = 138/1.15 = $120; do NOT subtract % from final value.
Percentage Points (pp)
Absolute difference between two percentage values; distinct from percentage change (relative); e.g., rate rising from 5% to 7% = +2 pp (absolute) but +40% change (relative).

Frequently Asked Questions

% increase = (new value − old value) / old value × 100. Steps: (1) Subtract old from new: difference = new − old. (2) Divide by old: difference / old. (3) Multiply by 100: × 100 = percentage. Example: bacterial colony count grew from 2 × 10⁵ to 8 × 10⁵: % increase = (8−2)/2 × 100 = 6/2 × 100 = 300%. A negative result indicates a percentage decrease: (150 − 200)/200 × 100 = −25% decrease.

New value = old value × (1 + percentage/100). Examples: $250 increases by 12%: new = 250 × 1.12 = $280. Population grows 7% per year from 10,000: after 1 year = 10,000 × 1.07 = 10,700. Compound growth over n years = old × (1 + rate/100)^n. After 3 years at 7%: 10,000 × (1.07)³ = 10,000 × 1.225 = 12,250. Each percentage point adds to the multiplier: 5% → ×1.05; 25% → ×1.25; 100% → ×2.0 (doubles); 200% → ×3.0.

Original = final / (1 + percentage/100). This is the inverse of applying an increase. Example: a product costs $138 after a 15% price increase — what was the original price? Original = 138 / 1.15 = $120. Common mistake: some people subtract 15% from $138: 138 × 0.85 = $117.30 → WRONG. The 15% was applied to the original price ($120), not to $138. The percentage increase was on a smaller base. Always divide by (1 + rate/100) to reverse, not subtract rate% from the final.

Percentage change: relative change expressed as a fraction of the original value × 100. Percentage points (pp): absolute difference between two percentage values. Example: unemployment rate falls from 8% to 5%. Percentage point change: 5 − 8 = −3 percentage points. Percentage change: (5−8)/8 × 100 = −37.5% change. Both descriptions are correct but mean different things. Why it matters: 'vaccination coverage increased from 40% to 60%' = +20 percentage points (the useful metric for public health). But '20 percentage points' is a 50% percentage change (20/40 × 100) — which sounds much larger. Media often confuse the two; always clarify which type of change is being reported.