Percent Increase Formula Calculators

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The percent increase formula calculates how much a value has grown relative to its original size: percent increase = ((new value − original value) / original value) × 100. A positive result indicates an increase; a negative result indicates a decrease (percent decrease). This calculation is fundamental in finance (return on investment, price changes), science (experimental changes, population growth), and everyday comparisons. A common error is dividing by the new value instead of the original — always divide by the starting value. The percent increase from A to B is not the same as the percent decrease from B to A.

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Percent Increase Formula

% increase = (new − original) / original × 100

Positive = increase; negative = decrease (% decrease = −result).

Examples: price rises from $80 to $100: % increase = (100−80)/80 × 100 = 25%. Population falls from 500 to 450: % change = (450−500)/500 × 100 = −10% (10% decrease).

Common Errors

  • Dividing by new value instead of original: (100−80)/100 = 20% (wrong; should be 25%)
  • Asymmetry error: 25% increase from 80 to 100; decreasing 100 by 25% gives 75, not 80. To return to 80 from 100: decrease = (100−80)/100 = 20% — a different percentage
  • Averaging percentages: two consecutive 10% increases ≠ 20% total. Actual: 1.10 × 1.10 = 1.21 = 21% total increase

Finding the Original Value

If you know the final value and percent increase: original = new / (1 + %/100). Example: after a 40% increase, price is $140. Original = 140 / 1.40 = $100. Never subtract the percentage of the new value.

Percentage Points vs. Percent Change

Tax rate from 20% to 25%: 5 percentage point increase (absolute). Percent change in rate = (25−20)/20 × 100 = 25% relative increase. Both correct but mean different things.

Glossary

Percent Increase
((new − original) / original) × 100; always divide by the original (starting) value; positive = increase; negative = decrease; the percent increase from A to B ≠ percent decrease from B to A.
Percentage Points
The arithmetic difference between two percentages (e.g., 20% to 25% = 5 percentage points); distinct from percent change (25% relative increase); specify which you mean to avoid ambiguity.
Original Value Recovery
To find the original from new value and percent increase: original = new / (1 + %/100); for decrease: original = new / (1 − %/100); never subtract the percentage from the new value.

Frequently Asked Questions

% increase = ((new value − original value) / original value) × 100. The original (starting) value is always the denominator. Positive result = increase; negative result = decrease (percent decrease). Examples: sales rise from 200 to 260 units: % change = (260−200)/200 × 100 = 30% increase. Temperature falls from 20°C to 15°C: % change = (15−20)/20 × 100 = −25% (25% decrease). Revenue from $4M to $3.4M: % change = (3.4−4)/4 × 100 = −15% decrease. Key: always use the original (starting) value in the denominator — not the new value, and not the average.

Percent change depends on the base (denominator), which is different in each direction. From 100 to 150: % increase = (150−100)/100 × 100 = 50%. From 150 to 100: % decrease = (100−150)/150 × 100 = −33.3%. The absolute change is the same (50 units) but the percent change is different because the base is 100 in the first case and 150 in the second. Consequence: a 50% price increase followed by a 50% price decrease does NOT return to the original price: $100 × 1.50 × 0.50 = $75 — a 25% net loss. You need a 100% increase to double, and a 50% decrease to halve — these are symmetric in value but asymmetric in percentage.

Original = new value / (1 + percent/100). If the new value is after a percent decrease: original = new value / (1 − percent/100). Examples: after a 25% increase, price is $125: original = 125 / 1.25 = $100. After a 20% decrease, enrollment is 400: original = 400 / (1 − 0.20) = 400 / 0.80 = 500. Common error: subtracting the percentage of the new value (wrong): $125 − 25% of $125 = $125 − $31.25 = $93.75 (incorrect; should be $100). Remember: the percent change was applied to the original, not the new value — divide by the factor, don't subtract the percentage.

Percentage point change: the arithmetic difference between two percentages. Percent change: how much one percentage changed relative to its original value (same formula as any other percent change). Example: unemployment rate falls from 6% to 4%: percentage point change = 4 − 6 = −2 percentage points. Percent change in unemployment rate = (4 − 6) / 6 × 100 = −33.3%. Both are correct but measure different things. Media often confuse the two: 'unemployment fell by 2%' (ambiguous — 2 percentage points or 2% relative?) vs. 'unemployment fell by 2 percentage points' (unambiguous) or 'unemployment fell by 33%' (relative change). Always specify whether you mean percentage points or percent change when discussing changes in percentages.