Percentage, Percent Change & Sale Discount Calculator

A percentage is a fraction with a fixed denominator

Per cent means 'per hundred'. A percentage is a fraction whose denominator is always 100, which is what makes percentages comparable across wildly different scales — 12% of a 30-person team and 12% of a 30-million population describe the same proportion.

Almost every real-world percentage question is one of four shapes, and the calculator handles all four side by side: a percentage of a value, the change between two values, a price after a discount, and the original price before one.

The four formulas

On this page's defaults: 15% of 250 is 37.5. Going from 100 to 135 is a 35% increase. An 80 price with 25% off costs 60, saving 20.

• Percent of a value = (percentage ÷ 100) × base value
• Percent change = ((new value − original value) ÷ original value) × 100
• Discounted price = original price − (original price × discount ÷ 100)
• Original price before a discount = discounted price ÷ (1 − discount ÷ 100)

Percent change versus percentage points

This is the most common piece of percentage confusion in news reporting and business writing, and it is worth getting straight.

If a rate moves from 10% to 15%, that is a rise of 5 percentage points — the simple difference between the two rates. It is also a rise of 50% — the relative change from the original value. Both statements are true and they describe the same event.

Which one to use depends on the question. Percentage points describe absolute movement in a rate (an interest rate, an unemployment rate, a conversion rate). Percent change describes proportional growth. Reporting a rate change only in percent, without saying which, is how a small movement gets made to sound enormous.

Stacked discounts never add up

Two sequential discounts are applied one after the other, each to the already-reduced price — they are never summed. Twenty percent off followed by a further 10% off is not 30% off; it is 28%, because the second discount is calculated on the smaller amount.

That asymmetry is why the reverse calculation matters too. If a shop advertises '20% off' and you know only the sale price, the original is the sale price divided by 0.8, not the sale price plus 20%. Adding 20% to the sale price overshoots by exactly the kind of margin that makes a 'great deal' look better than it was.

Percentage change from zero is undefined

Percentage change divides by the original value. When the original is zero the result is mathematically undefined, and no honest calculator can produce a number for it. Growth from 0 to 50 is not 'infinite percent' or '5000%' — it is a change from nothing, which percentages cannot express.

This tool reports that case as undefined rather than printing a confident 0%, because a 0% change and an undefined change are very different claims and only one of them is true.

Where the order of operations bites

Discounts apply to the gross price, and sales tax or VAT is then calculated on the reduced subtotal — not on the original price. Getting the order wrong inflates the tax you owe.

The same logic runs through payslips, invoices and quotes: identify the base, apply the percentage, then apply any further percentage to the new base. Whenever two percentages appear in the same sentence, the safe assumption is that they compound rather than add.

Practical uses

• Shopping and pricing — sale prices, stacked offers, and checking whether a 'was' price was ever real.
• Business and finance — margins, markups, growth rates, variance against budget, and commission.
• Everyday numeracy — a tip, a service charge, a rent increase, an interest rate change, a test score.
• Reports and analysis — converting a raw difference into a proportional one so two different-sized populations can be compared fairly.

Privacy

Every calculation runs in your browser. No value you type is transmitted, logged or placed in a URL — the page works with the connection switched off once it has loaded.