Percentage Calculator

What a percent actually is (and why the base matters)

Percent means 'per hundred', so 25% is simply 25 out of every 100, or the fraction 0.25. That part is easy. The reason percentages trip people up is the base — the number you are taking a share of. The exact same 20% can mean very different amounts depending on whether it applies to the original price, the sale price, or the after-tax total. So the first question to ask before any percentage calculation is never 'what is the rate' but 'a percent of what?' Fix the base clearly and almost every percentage problem becomes one of three routine calculations.

The three core calculations

• A percent of a number: number times percent divided by 100. Example: 18% of 1,200 is 1,200 times 18 divided by 100, which equals 216.
• What percent one number is of another (a ratio): part divided by whole, times 100. Example: 45 out of 180 is 45 divided by 180, which is 0.25, so 25%.
• Percentage change between two values: new minus old, divided by old, times 100. Example: going from 200 to 250 is 50 divided by 200, which is +25%; going from 250 back to 200 is -50 divided by 250, which is -20%.
• A quick shortcut: to add or remove a rate in one step, multiply. Adding 8% is times 1.08; taking 30% off is times 0.70.

A worked example, start to finish

Suppose a jacket is listed at 90 with 30% off. The discount is 90 times 30 divided by 100, which is 27, so you pay 90 minus 27, which is 63 — or more directly, 90 times 0.70 equals 63. Now imagine that 63 already includes 20% sales tax and you want the pre-tax amount. Do not subtract 20% of 63; the tax was calculated on the smaller pre-tax figure, not the total. Instead divide: 63 divided by 1.20 equals 52.50, and the tax portion is 63 minus 52.50, which is 10.50. Two different operations — multiply to add a rate, divide to strip one back out — and mixing them up is the single most common percentage error.

When you will reach for each one

• Shopping and discounts: multiply the price by (1 minus the discount rate) to get the final price directly, e.g. 90 times 0.70 for 30% off.
• Tax and tips: multiply a net amount by 1.10 to add 10% tax; to add a 15% tip to a 52.50 meal, 52.50 times 0.15 equals 7.88.
• Grades and test scores: divide points earned by points possible, e.g. 38 out of 50 is 0.76, or 76%.
• Investing and tracking gains: (current minus your entry) divided by entry shows how far up or down you are versus what you paid.
• Business pricing: markup and margin both compare price to cost but use different bases — a cost of 80 sold at 100 is a 25% markup (20 over 80) but only a 20% margin (20 over 100).

Common mistakes and misconceptions

• Percentage change is always measured against the OLD value, not the new one. Reversing the direction does not give the same percent.
• Stacked discounts do not add up. A 40%-off item taken a further 10% off is not 50% off: 100 becomes 60, then 60 becomes 54 — a total of 46% off, because the second cut applies to the reduced price.
• A discount then an equal markup does not restore the original. 20% off 100 is 80, then a 20% markup on 80 is 96, not 100, because the base changed between the two steps.
• Percentage points and percent are different. A rate moving from 20% to 25% is a 5 percentage-point rise but a 25% relative increase.
• 'Percent of' is not 'percent more'. 300% of 50 is 150, but a 300% increase on 50 gives 200 (the original 50 plus 150).

Reversing a percentage to find the original

A frequent real question is working backwards: you see a sale price and want the original, or you have a total and want the pre-tax figure. The rule is to divide by the multiplier rather than subtract. If 63 is a price after 30% off, the original is 63 divided by 0.70, which is 90 — you can check that 90 times 0.70 gives back 63. If a total of 63 includes 20% tax, the net is 63 divided by 1.20, which is 52.50. The mistake to avoid is taking the percentage of the final number: 30% of 63 is 18.90, which would wrongly suggest an original of about 81.90. Because the discount was applied to the larger original, you must undo it by dividing, not by subtracting a slice of the smaller result.

Cautions and limits

Percentages describe a proportion, not a fixed quantity, so a big-sounding percent on a tiny base can be trivial and a small percent on a huge base can be enormous — always keep the underlying amounts in view. Rounding also compounds: rounding each intermediate step can push a final total off by a cent or more, so round only at the end when accuracy matters. And a single percentage change never captures a sequence of changes; a +10% year followed by a -10% year leaves you at 99, not 100. This calculator handles one-step percent questions cleanly, but multi-period growth, compound interest, and tax brackets need their own logic rather than a lone percentage.