How do I calculate a percentage of a number?

Multiply the number by the percent as a decimal. For 15% of 80: 0.15 × 80 = 12. Or compute (15 ÷ 100) × 80. That’s the “X% of Y” mode.

How do I find what percent one number is of another?

Divide the part by the whole, then multiply by 100. Example: 12 is what percent of 80? (12 ÷ 80) × 100 = 15%.

What is the percent change formula?

Percent change = ((new − old) ÷ old) × 100. Use the original value in the denominator. A rise from 40 to 50 is +25%; a fall from 50 to 40 is −20%.

How do I reverse a percentage discount?

If you know the final price and the discount percent, divide the final by (1 − discount). After 25% off, final is 75% of original, so original = final ÷ 0.75.

Why isn’t 20% off then 10% off equal to 30% off?

Each discount applies to a new base. On $100, 20% off leaves $80; 10% of $80 is $8; you pay $72 — a 28% total reduction, not 30%.

Is the percentage calculator free?

Yes. Generatr’s percentage calculator runs in your browser for everyday percent, change, and reverse problems with no signup required.

How to Calculate Percentages (With Everyday Examples)

Percentages show a part of a whole as a fraction of 100. Once you know which question you’re asking — “what’s 15% of this bill?”, “what percent is 12 of 80?”, “how much did this grow?”, or “what was the price before the discount?” — the formula is short and the same every time.

This guide covers four everyday modes with worked numbers you can reuse for tips, sales, grades, stats, and personal finance. When you want instant answers, open the free percentage calculator and pick the mode that matches your question.

You’ll also see common mix-ups (percent vs percentage points, and “off” vs “of”) so a 20% sale doesn’t turn into a wrong cart total.

Free tool

Use the Percentage Calculator now

Open the interactive percentage calculator in your browser — free, instant, no signup.

Open Percentage Calculator

What Is a Percentage?

A percentage is a rate per hundred. “40%” means 40 per 100, or the decimal 0.40, or the fraction 40/100 = 2/5.

Convert freely

Percent → decimal: divide by 100 (18% → 0.18)
Decimal → percent: multiply by 100 (0.075 → 7.5%)
Fraction → percent: divide, then × 100 (3/8 = 0.375 → 37.5%)

Most calculator mistakes come from using 18 instead of 0.18 in a multiply step, or from picking the wrong whole (the base) when you ask “percent of what?”

Percent math shows up in loans and rates too — see how loan payments and interest work when you’re ready for amortization, not just a single percent of a number.

How Do You Calculate X% of Y?

Formula: result = (X ÷ 100) × Y. Same as X% × Y with X% written as a decimal.

Everyday examples

Tip: 18% of a $64 bill → 0.18 × 64 = $11.52
Sale: 25% of $80 → 0.25 × 80 = $20 off; pay $60
Tax: 7.5% of $120 → 0.075 × 120 = $9; total $129
Commission: 3% of $250,000 → 0.03 × 250,000 = $7,500

Mental shortcuts

10% of any number is the number with the decimal shifted one place left ($64 → $6.40). 5% is half of that. 15% ≈ 10% + 5%. 20% is double 10%. For 18%, take 20% then subtract 2% (0.02 × amount).

Run any “X% of Y” case in the free percentage calculator when the numbers get messy (taxes with three decimals, multi-item carts).

How Do You Find What Percent X Is of Y?

Formula: percent = (X ÷ Y) × 100. X is the part; Y is the whole.

Worked examples

Test score: 42 correct out of 50 → (42 ÷ 50) × 100 = 84%
Savings rate: saved $450 of $3,000 income → (450 ÷ 3000) × 100 = 15%
Win rate: 18 wins in 25 games → (18 ÷ 25) × 100 = 72%
Body metrics: if weight dropped 4 lb from 180, that 4 is (4 ÷ 180) × 100 ≈ 2.2% of starting weight

Order matters

Always divide part by whole. “What percent is 50 of 40?” is (50 ÷ 40) × 100 = 125% — more than the whole, which is allowed when X > Y. If you swap the numbers, you’ll invent a fake percentage under 100%.

Tracking weight or BMI changes? Pair percent change with the BMI calculator and our BMI guide for height-adjusted context.

How Do You Calculate Percent Increase or Decrease?

Formula: percent change = ((new − old) ÷ old) × 100. Positive means increase; negative means decrease.

Examples

Price rise: $40 → $50 → ((50 − 40) ÷ 40) × 100 = +25%
Price drop: $50 → $40 → ((40 − 50) ÷ 50) × 100 = −20%
Followers: 1,200 → 1,500 → ((1500 − 1200) ÷ 1200) × 100 = +25%

Notice $40→$50 is +25%, but $50→$40 is only −20%. Percent change is not symmetric because the denominator (the starting value) changed.

Percentage points vs percent

If an interest rate moves from 4% to 5%, that’s a 1 percentage point rise, but a 25% relative increase ((5−4)÷4). News and finance mix these constantly — check which one you need.

Loan and mortgage rates are classic cases where a 0.5-point change is small in percentage points but huge in dollars over 30 years. See how mortgage payments are calculated for the payment side.

How Do You Work Backwards From a Percentage?

Reverse percentage asks: “If this amount is X% of the original, what was the original?” Formula: original = final ÷ (X ÷ 100).

Discount reverse

A shirt costs $60 after 25% off. Then $60 is 75% of the original. Original = 60 ÷ 0.75 = $80.

Tax reverse

Total is $86.40 including 8% tax. The total is 108% of the pre-tax price. Pre-tax = 86.40 ÷ 1.08 = $80.

Tip included reverse

You paid $92 total with an 15% tip included on food. Total is 115% of the food bill. Food = 92 ÷ 1.15 = $80.

Common trap

After a 20% increase, undoing it is not “subtract 20% of the new number” if you want the old number with one step — divide by 1.20 instead. 100 → 120 is +20%; 120 × 0.80 = 96, which is wrong. 120 ÷ 1.20 = 100, which is right.

How Do Stacked Discounts, Tips, and Taxes Combine?

Apply percentages in the order the real world applies them. Order changes the dollar result when discounts stack.

Two discounts: 20% off then 10% off is not 30% off. On $100: after 20% → $80; after 10% → $72. True combined discount = 28% off, not 30%.
Tax then tip vs tip then tax: restaurants differ. Many people tip on pre-tax food; some tip on the post-tax total. Pick a policy and stay consistent.
Markup then discount: a 50% markup from cost $40 → $60 list; 20% off list → $48 — still above cost.

Quick multi-step checklist

Write the base amount.
Convert each percent to a multiplier (1 − d for discount d, 1 + t for tax t).
Multiply in chronological order.
Round money to cents at the end (or as the register does).

When you’re splitting a bill or checking a receipt, the free percentage calculator keeps each step honest.

What Percentage Mistakes Should You Avoid?

Small formula slips create big wrong answers on prices and stats.

Using the wrong base — percent of the original vs percent of the sale price
Adding percents that should multiply — stacked discounts aren’t simple sums
Confusing points and percent — 2% → 3% is +1 point, not “+1% relative” in casual speech alone
Forgetting 100 when converting — leaving a ratio like 0.18 unlabeled as “18%”
Dividing by the new value for percent change — always divide by the old value for standard percent change

Percent tools also support calorie and body-weight tracking (for example “protein is what percent of calories”). For daily energy targets, see the daily calorie needs guide.

Practice with numbers you care about — last receipt, last paycheck, last exam — so the four modes stick.

Step-by-Step Instructions

1Open the free percentage calculator on Generatr.
2Choose the mode that matches your question (X% of Y, X is what % of Y, change, or reverse).
3Enter the known values carefully — part, whole, old, new, or final amount.
4Convert percents to decimals mentally (15% → 0.15) if you’re checking by hand.
5Read the result and label it (dollars, points, percent, etc.).
6For multi-step problems, apply one percentage at a time in real-world order.
7Double-check the base: are you taking a percent of the original or of a new total?
8Rerun with rounded and unrounded inputs if money is involved so cents match the receipt.