Math

Percent Calculator

Percent problems come in three flavors and people mix them up constantly. "What's 18% of $54?" is one calculation. "$9.72 is what percent of $54?" is a different calculation. "Sales went from $54k to $63k — what's the percent change?" is a third. This calculator handles all three modes — pick the one that matches your question, plug in two numbers, get the answer instantly. Useful for tipping, calculating sales tax, figuring out discounts, comparing year-over-year revenue, computing grade percentages, checking that a markup is what you actually want, and any other "percent something" question that comes up. Works with decimals, negative numbers, and very large or very small values.

Enter two numbers to see your answer.

Quick examples

15% of 80

25 is what % of 200?

12.5%

% change 50 → 65

+30%

How it works — the three formulas

X% of Y = (X ÷ 100) × Y

X is what % of Y = (X ÷ Y) × 100

% change A → B = ((B − A) ÷ A) × 100

All three formulas share the same idea: percent ("per cent" = "per hundred") is just a fraction multiplied by 100. The word "of" means multiplication. The word "is" means equals.

Worked example — Mode 1: 20% of 150. (20 ÷ 100) × 150 = 0.20 × 150 = 30. Useful for sales tax (6.5% of $42), tips (18% of $54), or discounts (25% off $89).

Worked example — Mode 2: 30 is what percent of 150? (30 ÷ 150) × 100 = 20%. Useful for grades (got 27 out of 35 on a quiz), commission rates ($1,400 commission on $20,000 in sales), or "what fraction of my salary is rent?"

Worked example — Mode 3: percent change from 50 to 65. ((65 - 50) ÷ 50) × 100 = +30%. Useful for sales growth, weight loss, investment returns, or year-over-year comparisons. A negative result means a decrease (50 → 40 = -20%).

How to use this calculator

Pick the mode that matches your question. The X and Y labels change to guide you.
"X% of Y": X is the percent (e.g. 18), Y is the total (e.g. 54). Result is the part.
"X is what % of Y": X is the part, Y is the total. Result is the percent.
"% change A → B": A is the starting value, B is the ending value. Result is the percent change, signed.
Decimal inputs are fine — enter 7.25 for sales tax, 18.5 for a tip.

Common scenarios

Tipping at a restaurant. Bill is $87.40. You want to tip 20%. Use Mode 1: 20% of 87.40 = $17.48. Round to $17 (cheap) or $18 (standard) or $20 (generous on round-up). Pro tip: tip on pre-tax in most states; tip on post-tax is fine too — small dollar difference.

Discount math. $129 shirt, 30% off. Use Mode 1: 30% of 129 = $38.70 off. Final price: $90.30 (or just take 70% of 129 directly = $90.30). For "buy one get one 50% off" on two $50 items: total $75 = 25% off the pair effectively.

Test score percentages. Got 37 out of 50 on a quiz. Use Mode 2: 37 is what % of 50 = 74%. Below the typical B threshold; time to study. For weighted gradebook: convert each assignment to a percentage, multiply by its weight, sum.

Salary raise. Old salary $58,000, new salary $63,500. Use Mode 3: percent change = ((63,500 - 58,000) ÷ 58,000) × 100 = +9.48%. Above inflation, which is the actual benchmark of a "real" raise. A 3% raise in a 4% inflation year is a pay cut.

Investment returns. Invested $5,000 in January. Worth $5,840 in December. Use Mode 3: ((5,840 - 5,000) ÷ 5,000) × 100 = +16.8%. Beat the S&P 500 average that year.

FAQ

What's the difference between percent change and percent difference? +

Percent change has a direction (A → B) and a sign — going from 100 to 80 is -20%, going from 80 to 100 is +25% (different magnitudes!). Percent difference is symmetric, used when neither value is a baseline: |A - B| ÷ ((A + B) ÷ 2) × 100. Most everyday questions are percent change.

Why are increase and decrease percentages asymmetric? +

Because the baseline changes. Going from 100 to 80 is a 20% decrease (20 out of 100). Going from 80 back to 100 is a 25% increase (20 out of 80). A 50% off sale followed by a 50% increase doesn't get you back to the original — you'd need a 100% increase to recover.

How do I calculate a tip? +

Use Mode 1 ("X% of Y"). Enter the tip percentage (e.g. 18), then the pre-tax bill total. The result is the tip amount. For a quick mental shortcut: 10% is moving the decimal one left; double it for 20%; halve the 10% for 5%; sum for 15%. So 15% of $48 = $4.80 + $2.40 = $7.20.

How do I calculate a discount? +

Use Mode 1 to get the discount dollars, then subtract from original. Or compute (100% - discount%) directly: 25% off means you pay 75%. For $80 item at 25% off: 75% of 80 = $60. Faster than computing the discount and subtracting.

What about stacked or compounded discounts? +

Multiply, don't add. "30% off, then extra 20% off" doesn't equal 50% off — it's 0.70 × 0.80 = 0.56 = 44% off the original. Common retail trick to make stacked discounts sound bigger than they are. Real coupons stack multiplicatively unless stated otherwise.

How do I calculate sales tax? +

Use Mode 1: tax rate × pre-tax total. Ohio 7.5% on a $42 purchase: 7.5% of 42 = $3.15 tax, $45.15 total. For "what's the pre-tax price if total is $45.15 including 7.5% tax?": divide total by 1.075 = $42.

Can I use this for percentage points vs percent change? +

Be careful with the distinction. Going from 5% interest rate to 7% interest rate is a 2 percentage point increase, but a 40% relative increase. News and politics often blur these — "Federal funds rate raised 25 basis points" is a 0.25 percentage point hike, not 25%.

What if I need to find the original value before a percentage was added? +

"Reverse percent" problem. If $107 includes 7% tax, original = 107 ÷ 1.07 = $100. If $63 is after a 30% markup, original cost = 63 ÷ 1.30 = $48.46. General rule: total ÷ (1 + decimal rate) = pre-increase value.

What's a basis point? +

1 basis point = 0.01% = 0.0001. Used in finance for precision (a 25 bps rate cut = 0.25%). 100 bps = 1 percentage point. Common in mortgages, bonds, and central bank language.