Percentages are everywhere — sale discounts, restaurant tips, taxes, exam scores and loan interest. The good news: every percentage problem is solved with the same simple idea. This guide teaches you five reliable methods to calculate any percentage by hand, each with a worked example, plus mental-math shortcuts you can use at the checkout counter.
The word percent literally means per hundred. So 15% is just 15 out of every 100. Every percentage calculation is a variation of one relationship:
percentage = (part ÷ whole) × 100
Once you can rearrange this one formula, you can solve any percentage problem — finding a part, finding the percentage itself, or working backwards to the original number. Let's go through each method.
This is the most common percentage question: what is 15% of 240?
Formula: (percentage ÷ 100) × number
Worked example: 15% of 240
So 15% of 240 is 36. Use this for tips (18% of an $84 bill), tax, commission and exam marks.
Question: 36 is what percent of 240? This is the formula in its original form.
Formula: (part ÷ whole) × 100
Worked example: 36 ÷ 240 = 0.15, then 0.15 × 100 = 15%.
This is the method behind statements like “you scored 82%” — your marks divided by total marks, times 100. Try it with our percentage calculator to check your working.
Question: a price rises from $80 to $100 — what is the percentage increase?
Formula: ((new value − old value) ÷ old value) × 100
Worked example:
The key detail: always divide by the original value, not the new one. This method works for salary hikes, population growth and investment returns.
Question: a $120 jacket is on sale for $90 — what is the discount percent?
Formula: ((old value − new value) ÷ old value) × 100
Worked example:
For shopping math specifically, our discount calculator also shows the final sale price and your total savings.
Question: after a 25% discount you paid $90 — what was the original price? This one trips people up, because you can't just add 25% back.
Formula: final value ÷ (1 − percentage ÷ 100)
Worked example: 90 ÷ (1 − 0.25) = 90 ÷ 0.75 = $120.
Why not “add 25%”? Because 25% of $90 is $22.50, giving $112.50 — wrong. The discount was 25% of the original price, not the sale price. Reverse percentages are also how you work backwards from a tip-included bill or a tax-inclusive total.
You don't always need a calculator. These shortcuts handle most everyday percentages:
It also helps to know common fraction equivalents:
So 25% off $80 is just a quarter of 80 = $20 off, sale price $60. No calculator needed.
Master the five methods above and you'll never be confused by a percentage again — and when you want the answer in one tap, the free percentage calculator is right here.
Skip the manual math — enter any numbers and get the answer instantly, with the formula shown step by step.
For most everyday numbers, use the 10% trick: move the decimal point one place left to get 10%, then combine (10% + 5% = 15%, double 10% = 20%). For exact answers, use (percentage ÷ 100) × number — or the free percentage calculator on this site.
Subtract the old value from the new value, divide by the old value, and multiply by 100: ((new − old) ÷ old) × 100. For example, 80 to 100 is a 25% increase.
Divide the sale price by (1 − discount ÷ 100). A $90 item after 25% off was originally 90 ÷ 0.75 = $120. Don't just add the percentage back — that gives the wrong answer.
A change from 10% to 15% is a 5 percentage-point increase, but a 50% relative increase (5 ÷ 10). News about interest rates usually means percentage points.
Yes. It just means the part is bigger than the whole — e.g., 150% of a target, or 200% growth means tripling (original + 2× original).
Learn the 10%/5%/1% decimal-shift tricks and common fraction equivalents (25% = 1/4, 20% = 1/5). They cover nearly all everyday percentage math.
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