Percentage Calculator

The formulas behind each mode

Every percentage problem is just a variation of one core relationship: Part = (Percentage / 100) × Whole. The different modes rearrange this formula to solve for whichever piece you're missing.

X% of Y: Result = (X ÷ 100) × Y. So 15% of 200 = (15 ÷ 100) × 200 = 30.

X is what % of Y: Percentage = (X ÷ Y) × 100. So 30 is what % of 200? (30 ÷ 200) × 100 = 15%.

Percentage change (increase or decrease): Change = ((New − Old) ÷ Old) × 100. A positive result means an increase, negative means a decrease. So going from 80 to 100: ((100 − 80) ÷ 80) × 100 = 25% increase.

Applying a percentage increase: New Value = Original × (1 + Percentage ÷ 100). A 10% raise on 50,000 = 50,000 × 1.10 = 55,000.

Applying a percentage decrease: New Value = Original × (1 − Percentage ÷ 100). A 25% discount on 400 = 400 × 0.75 = 300.

Reverse percentage (after increase): Original = Final ÷ (1 + Percentage ÷ 100). If the price after a 20% markup is 1,200, original = 1,200 ÷ 1.20 = 1,000.

Reverse percentage (after decrease): Original = Final ÷ (1 − Percentage ÷ 100). Price after 20% discount is 800, original = 800 ÷ 0.80 = 1,000.

One thing worth knowing: percentage change and percentage points are different. If an interest rate goes from 4% to 6%, that's a 2 percentage point increase but a 50% increase in relative terms. This calculator handles the percentage change calculation (relative).