Percentage Calculator

About Percentage Calculator

Almost every percentage problem is one of four questions: what percent is A of B (A ÷ B × 100), what is X% of B (B × X ÷ 100), how much did something change from an old value to a new one ((new − old) ÷ old × 100), and what is the price after a discount. The calculator puts each on its own tab. A negative discount rate is treated as a markup, and a percent change from zero returns nothing, because dividing by zero has no meaning.

The formulas are easy. Mistakes come from picking the wrong base, the number you divide by. Nearly every confusing headline, sale sign or interest-rate story that misleads people does so by quietly switching the base.

Percent versus percentage point

If a central bank raises its rate from 3.00% to 3.50%, it rose by 0.5 percentage points (financial news often says 50 basis points). As a relative change it rose 16.7%. Unemployment going from 4% to 5% is a 1-point rise and a 25% rise. Both statements are true, and they leave very different impressions.

When the quantity is already a percentage, such as a rate, a poll share or a market share, report the gap in points and the relative change in percent. If a headline says turnout grew 10%, check whether it went from 60% to 70% (10 points) or from 60% to 66% (10 percent). Entering 3 and 3.5 on the Change tab gives 16.67%, the relative answer.

Down 50% then up 50% is not break-even

Percent change always divides by the earlier value, so the base shifts between the fall and the rise. A $1,000 stock that drops 50% is worth $500; a 50% gain from there brings it to $750. Getting back to $1,000 takes a 100% gain.

Smaller moves behave the same way: +10% then −10% leaves you at 0.99, −20% then +20% at 0.96. After a loss L, the gain needed to recover is L ÷ (1 − L): 11.1% after a 10% loss, 42.9% after 30%, 100% after 50%, 400% after 80%.

This is also why averaging percent changes misleads. A fund that returns +50% one year and −50% the next has an arithmetic average of 0% but ends at 0.75 of where it started, an annualized return of √0.75 − 1 ≈ −13.4%.

Working backwards: pre-discount prices and sales tax

If an item costs $80 after 20% off, the original price is $80 ÷ 0.8 = $100, not $80 × 1.2 = $96. Twenty percent of the sale price and twenty percent of the original are different amounts. The same trap appears with tax: in a country with 20% VAT, a £120 VAT-inclusive price contains £20 of VAT (120 ÷ 1.2 × 0.2), not £24.

You can check a reverse calculation on the 'What percent' tab: 80 ÷ 100 = 80% confirms that $80 is the price after 20% off $100. The same method recovers a salary before a raise: $66,000 after a 10% raise came from $60,000, not $59,400.

Stacked discounts and growth rates multiply

An extra 20% off an item already marked down 30% is not 50% off. The coupon applies to the reduced price, so the total is 1 − 0.7 × 0.8 = 44%. Run the Discount tab twice to see it: $100 → $70 → $56.

Growth works the same way. Three years of 10% growth is 1.1³ − 1 = 33.1%, not 30%. Turning 33.1% over three years back into an annual rate needs the cube root (10%), not division by three (11%). Prices rising 3% a year for ten years add up to 34.4%, which is why a decade of modest inflation feels larger than the yearly numbers suggest.

Common misreadings in the news

• “Risk up 50%”: going from 2 in 10,000 to 3 in 10,000 is a 50% relative increase but an absolute rise of 0.01 percentage points. Look for the absolute numbers.
• “Up 200% on last year” means three times as much. Double is a 100% increase.
• Base effects: comparing with a month that collapsed a year earlier makes this year's growth look dramatic. Try swapping in a different starting value on the Change tab.
• “Halved, then doubled” returns to the start; “down 50%, up 50%” ends at 75%.
• “Up to 70% off” describes the best single item, not the typical discount.

Worked examples

How to use it

1. Pick the tab that matches your question: what percent, X% of a number, percent change, or discount.
2. Enter the two values; for percent change, enter the earlier value first.
3. On the Discount tab, a negative rate gives the price after a markup.

Frequently asked questions