Percentage Calculator

Percentage Calculator: solve percentage problems step-by-step. Clear formula, worked example, and FAQs included.

A percentage calculator solves the common variations of percentage arithmetic: calculating what percentage one number is of another, finding a percentage of a given number, and calculating percentage increase or decrease between two values. Percentage literacy is fundamental to understanding discounts, tax rates, interest rates, statistical reporting, nutritional information, scientific data, and financial statements. Despite being a core numeracy skill, percentage calculations are frequently misapplied — particularly percentage change calculations and the difference between percentage points and percentage changes. Loan Payment Calculator and Mortgage Calculator are closely related tools.

The most common percentage errors in everyday life include: confusing a 20% discount on a discounted price vs the original price; misunderstanding that a 50% fall followed by a 50% rise does not return to the starting value (it reaches only 75%); and mixing up percentage change with percentage point change. In statistics and economics, these distinctions are critical: a central bank raising interest rates from 2% to 2.5% is a 0.5 percentage point increase but a 25% percentage change in the rate — two entirely different meanings.

For "X is what % of Y": enter both numbers and the calculator divides X by Y and multiplies by 100.
For "X% of Y": enter the percentage and the base number; the result is the percentage amount.
For percentage increase/decrease: enter the original value and new value; the result shows the % change.
For reverse percentage (finding original value before a % was added or removed): enter the final amount and the percentage applied.
Check whether you need the percentage change from original to new, or from new to original — these are different calculations with different results.
For compound percentage changes, do not add sequential percentages — multiply the factors: a 10% increase then a 10% decrease = 1.10 × 0.90 = 0.99, a net 1% decrease.

Percentage formulas

X is what % of Y: (X ÷ Y) × 100

X% of Y: (X ÷ 100) × Y

% change from A to B: ((B − A) ÷ A) × 100

Original value before X% added: Final ÷ (1 + X/100)

Original value before X% removed: Final ÷ (1 − X/100)

Worked examples: 45 is what % of 180? (45 ÷ 180) × 100 = 25%. 15% of 240? 0.15 × 240 = 36. Price rose from 80 to 96 — % increase: ((96−80) ÷ 80) × 100 = 20%. Price was 120 after 20% tax added — original pre-tax: 120 ÷ 1.20 = 100.

Reading percentage results correctly

Percentage point vs percentage change

A critical distinction: percentage point change is the arithmetic difference between two percentages (if unemployment rises from 4% to 6%, that is a 2 percentage point increase). Percentage change is the proportional change in the percentage value itself (a rise from 4% to 6% is a 50% increase in the unemployment rate). Financial journalism, economic reporting, and political debate frequently conflate these — reading carefully for which meaning is intended is essential for accurately interpreting reported data.

Math tips and best practices

Always identify the base (denominator) in a percentage statement — "20% cheaper than what?" and "20% increase from which starting point?" give very different results.
Avoid adding sequential percentages — a 30% discount followed by a further 20% off is not 50% off; it is 1 − (0.70 × 0.80) = 44% off the original price.
When reversing a tax-inclusive price, divide by (1 + tax rate) — do not subtract the tax rate percentage from the inclusive price, which underestimates the tax component.
For percentage change comparisons, always state the base year or reference value to avoid cherry-picking base periods that exaggerate changes.
In financial returns, percentage changes are asymmetric: a 50% loss requires a 100% gain to recover, not 50%.

A 50% price reduction followed by a 50% price increase returns to only 75% of the original price — not the original value.
A 1% difference in annual investment return compounded over 30 years changes the final portfolio value by approximately 34%: 1.07³⁰ = 7.6× vs 1.06³⁰ = 5.7×.
If a sale item is "30% off" and a further "10% off the sale price" is applied, the total discount is 37%, not 40%: (1 − 0.70 × 0.90) = 37%.
Percentage point changes in central bank interest rates of 0.25% represent 25 basis points — financial markets price assets to many decimal places using this unit.

Common mistakes to avoid

Adding sequential discounts or increases arithmetically instead of multiplicatively — always convert to multipliers and multiply them together.
Calculating reverse tax by subtracting the tax rate from a tax-inclusive price — divide by (1 + rate) instead.
Confusing percentage point changes with percentage changes in economic and statistical contexts.
Misidentifying the base in percentage increase calculations — "increased by 20%" requires clarity on whether that is 20% of the original value or some other reference point.

Percentage calculations in commercial contexts are governed by consumer protection and trading standards law in each jurisdiction. Most countries require that sale discounts are calculated against a genuine pre-sale reference price that reflects actual selling history. Tax calculations using percentage formulas must follow the precise rules set by the relevant tax authority. This calculator is for informational and educational purposes only.