Free percentage calculator with three modes: find X% of Y, work out what percent X is of Y, and calculate percentage increase or decrease — with every step shown.
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Three modes: (1) X% of Y = (X ÷ 100) × Y. (2) X is what % of Y = (X ÷ Y) × 100. (3) Percentage change = ((New − Old) ÷ Old) × 100; a positive answer is an increase, negative a decrease.
A percentage is just a fraction of 100: 45% means 45 out of every 100, or the decimal 0.45. Every question this calculator answers is one of three formulas. Mode 1 — X% of Y: (X ÷ 100) × Y. Example: what is 15% of 80? (15 ÷ 100) × 80 = 0.15 × 80 = 12. Mode 2 — X is what % of Y: (X ÷ Y) × 100. Example: 42 is what % of 50? (42 ÷ 50) × 100 = 84%. Mode 3 — percentage change from X to Y: ((Y − X) ÷ X) × 100. Example: from 100 to 125: ((125 − 100) ÷ 100) × 100 = 25%. Choose the mode that matches how your question is phrased and the calculator shows each step of the working.
1. Pick the calculation type that matches your question: 'X% of Y' for tips, discounts and parts of a total; 'X is what % of Y' for grades and shares; or 'percent_change' for increases and decreases. 2. Type the two numbers — results update instantly. 3. Read the formula line shown with the answer to confirm you picked the right mode. 4. In percent-change mode, check the tag: a positive result means an increase, a negative result means a decrease, and zero means no change. Example: 36 out of 48 on a quiz, in 'X is what % of Y' mode, gives (36 ÷ 48) × 100 = 75%.
Percentage change measures how much a value grew or shrank relative to where it started: ((New − Old) ÷ Old) × 100. The sign tells the story. A price rising from $100 to $125: ((125 − 100) ÷ 100) × 100 = +25%, a 25% increase. A price falling from $80 to $60: ((60 − 80) ÷ 80) × 100 = −25%, a 25% decrease. Website traffic growing from 4,000 to 5,200 visits: ((5,200 − 4,000) ÷ 4,000) × 100 = 30% increase. A salary going from $3,000 to $3,450: ((3,450 − 3,000) ÷ 3,000) × 100 = 15% increase. Remember the divide is always by the OLD (original) value — dividing by the new value is the most common error.
A move from 20% to 25% is a 5 percentage-point rise — but a 25% relative increase: (25 − 20) ÷ 20 × 100 = 25%. Percentage points describe the raw gap between two percentages; percent describes the gap relative to the starting value. News reports and statistics usually mean percentage points, so 'tax rose 5%' and 'tax rose 5 percentage points' are very different claims. When you hear an interest rate moved from 10% to 15%, that is a 5 percentage-point increase but a 50% relative increase.
Percentage change compares a new value to an old starting value, so it has a direction. Percentage difference compares two values with no 'before' and 'after' — it measures the gap relative to their average: (|A − B| ÷ ((A + B) ÷ 2)) × 100. Comparing 60 and 80: |60 − 80| ÷ ((60 + 80) ÷ 2) × 100 = 20 ÷ 70 × 100 ≈ 28.57%. The percentage difference is always symmetric — it is 28.57% whether you go from 60 to 80 or from 80 to 60 — while the percentage change would be +33.33% one way and −25% the other. Use change for growth over time; use difference when neither value is the baseline.
Reverse percentage problems start from the final value and a rate, and ask for the starting value. The formula is Original = Final ÷ (1 ± Percentage ÷ 100) — use minus for a decrease and plus for an increase. '30 is 20% of what number?' → 30 ÷ (20 ÷ 100) = 30 ÷ 0.20 = 150. You paid $60 after a 25% discount — what was the original price? 60 ÷ (1 − 0.25) = 60 ÷ 0.75 = $80. A bill of $89.60 after a 12% price rise started at 89.60 ÷ 1.12 = $80. The key is dividing by (1 ± the decimal rate), not subtracting the percent from the final number.
Percentages can exceed 100% — +200% means tripling the original (2× gain), and +100% means doubling. Convert between forms freely: a fraction becomes a percent by dividing and multiplying by 100 (3 ÷ 4 × 100 = 75%); a decimal becomes a percent by multiplying by 100 (0.45 = 45%). Going the other way, divide the percent by 100: 18% = 0.18. The multiplier view is handy: increasing by 50% is ×1.5, decreasing by 20% is ×0.8, and a 25% decrease followed by a 25% increase does NOT return you to the start (0.75 × 1.25 = 0.9375, so you end up 6.25% down).
1. Dividing the wrong way in 'what percent' problems — it is always part ÷ whole: 36 ÷ 48 for '36 is what % of 48', never 48 ÷ 36. 2. Calling a rise from 20% to 25% 'a 5% increase' — that is 5 percentage points, a 25% relative increase. 3. Adding successive percentages: two 10% discounts in a row take off 19% in total, not 20%, because the second discount applies to the already-reduced price (0.9 × 0.9 = 0.81). 4. Using the wrong base in percentage change — always divide by the old value, not the new one. 5. Confusing percentage difference (average-based, symmetric) with percentage change (old-value-based, directional).
Discounts: a $150 jacket with 20% off saves 0.20 × 150 = $30, so you pay $120. Tips: an 18% tip on a $64 bill is 0.18 × 64 = $11.52. Grades: 42 out of 50 on an exam is (42 ÷ 50) × 100 = 84%. Pay raises: $50,000 to $55,000 is ((55,000 − 50,000) ÷ 50,000) × 100 = 10%. Sales tax: 8% on a $50 purchase adds 0.08 × 50 = $4. Data and surveys: 30 out of 150 respondents is (30 ÷ 150) × 100 = 20%. The same three formulas cover shopping, dining, schoolwork, finance and data analysis — anywhere you compare a part to a whole or a new value to an old one.
Multiply the number by the percentage divided by 100: (X ÷ 100) × Y. For example, 20% of 150 is (20 ÷ 100) × 150 = 0.20 × 150 = 30. Use the 'X% of Y' mode for tips, discounts and tax.
Divide the first number by the second and multiply by 100: (X ÷ Y) × 100. For example, 45 is (45 ÷ 180) × 100 = 25% of 180, and a 42-out-of-50 exam score is (42 ÷ 50) × 100 = 84%.
Subtract the old value from the new value, divide by the old value, and multiply by 100: ((New − Old) ÷ Old) × 100. Going from 50 to 75: ((75 − 50) ÷ 50) × 100 = 50% increase.
Use the same percentage change formula — the result comes out negative, which means a decrease. Going from 80 to 60: ((60 − 80) ÷ 80) × 100 = −25%, i.e. a 25% decrease.
A move from 20% to 25% is a 5 percentage-point rise but a 25% relative increase ((25 − 20) ÷ 20 × 100). Percentage points measure the raw gap between two rates; percent measures the gap relative to the starting value.
Divide the final value by (1 ± the decimal rate): Original = Final ÷ (1 − rate) for a decrease, Final ÷ (1 + rate) for an increase. If you paid $60 after a 25% discount, the original price was 60 ÷ 0.75 = $80.
Percentage change compares a new value to an old baseline: ((New − Old) ÷ Old) × 100. Percentage difference has no baseline — it compares two values against their average: (|A − B| ÷ ((A + B) ÷ 2)) × 100. Comparing 60 and 80 gives a 28.57% difference, symmetric in both directions.
Divide the fraction and multiply by 100, or multiply a decimal by 100. 3/4 = 0.75 = 75%, and 0.45 = 45%. To go back, divide the percent by 100: 18% = 0.18.
Yes. A percentage is just a ratio to 100, so +100% means doubling the original value and +200% means tripling it. A value can also grow more than 100% — for example, traffic rising from 4,000 to 9,000 visits is a 125% increase.
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