Calculate percentages in common phrases, three-way percentage equations, percentage differences, and percentage increases/decreases with step-by-step mathematical breakdowns.
Enter any two values to automatically compute the third: [P] % of [V₁] = [V₂]
Select any of the three natural language percentage phrases to compute exact values instantly.
Computes relative percentage difference between two values relative to their average: |V₁ - V₂| / ((V₁ + V₂) / 2) × 100
Enter any two fields to solve the third: initial value, percentage increase/decrease, or final value.
| Percentage | Decimal Multiplier | Fraction Form | Calculation Example ($100 base) |
|---|---|---|---|
| 1% | 0.01 | 1/100 | $1.00 |
| 5% | 0.05 | 1/20 | $5.00 |
| 10% | 0.10 | 1/10 | $10.00 |
| 15% | 0.15 | 3/20 | $15.00 |
| 20% | 0.20 | 1/5 | $20.00 |
| 25% | 0.25 | 1/4 | $25.00 |
| 33.33% | 0.3333... | 1/3 | $33.33 |
| 50% | 0.50 | 1/2 | $50.00 |
| 75% | 0.75 | 3/4 | $75.00 |
| 100% | 1.00 | 1/1 | $100.00 |
The term percentage originates from the Latin per centum, meaning "by the hundred". A percentage is a dimensionless ratio or fraction with a fixed denominator of 100, symbolized by the % sign.
To find P percent of total V₁:
Relative change from initial value V₁ to final V₂:
Difference compared to the midpoint average:
Adding percentage tax or markup to net price:
Percentage change measures the directional shift from an established starting initial value to a new value (e.g. inflation, stock returns, price increase). Percentage difference compares two values that do not have a chronological order, measuring deviation relative to their average.
Subtract the old value from the new value, divide by the absolute value of the old value, and multiply by 100. A positive result indicates an increase, while a negative result indicates a decrease.
Yes. While percentages of a whole finite object cannot exceed 100% in proportions, rates of growth and change frequently exceed 100%. For example, doubling a value represents a 100% increase (200% of the original).
Multiply the original price by (1 - Discount% / 100). For instance, a $60 item with a 20% discount is $60 × (1 - 0.20) = $60 × 0.80 = $48.
A percentage represents a ratio divided by a base amount. Dividing by zero is mathematically undefined because no quantity multiplied by zero can equal a non-zero number.