Calculate a percentage of a number, find what percent one number is of another, apply or reverse a percentage change, and compare values using percentage change or percentage difference.
Each mode reports missing values, division by zero, or a reverse decrease of 100% or more directly beside its inputs.
Result = (P ÷ 100) × N
P is the percentage and N is the number. Use it to find a portion.
Percentage = (A ÷ W) × 100
A is the part and W is the non-zero whole. Use it for ratios, scores, and shares.
Final = O × (1 ± P ÷ 100)
O is original and P is the change rate. Add for an increase; subtract for a decrease.
Original = F ÷ (1 ± P ÷ 100)
F is final and P is the prior change rate. Add for an increase; subtract for a decrease.
Change % = ((N − O) ÷ O) × 100
O is the non-zero original and N is new. The original value is the denominator.
Difference % = |A − B| ÷ ((|A| + |B|) ÷ 2) × 100
A and B are peers. Their average magnitude is the denominator, so neither is treated as original.
Scenario: Find 20% of £150.
20 ÷ 100 × 150 = 30
The percentage is 20, the number is 150, and the result is £30.
Scenario: 45 correct answers out of 180.
45 ÷ 180 × 100 = 25%
The part is 45 and the whole is 180, so the score is 25%.
Scenario: Salary rises from £32,000 to £36,000.
(36,000 − 32,000) ÷ 32,000 × 100 = 12.5%
The original is £32,000, the new value is £36,000, and the increase is 12.5%.
Scenario: Usage falls from 500 to 425 units.
(425 − 500) ÷ 500 × 100 = −15%
The original is 500 and the final value is 425, a 15% decrease.
Scenario: Add 15% to a £120 item.
120 × (1 + 15 ÷ 100) = 138
The original is £120, the increase is £18, and the final value is £138.
Scenario: Take 20% off an £80 item.
80 × (1 − 20 ÷ 100) = 64
The original is £80, the discount is £16, and the final price is £64.
Scenario: A final price is £92 after a 20% discount.
92 ÷ (1 − 20 ÷ 100) = 115
The final value is £92 and the original price was £115.
Scenario: Compare measurements 80 and 100 with no baseline.
|80 − 100| ÷ ((80 + 100) ÷ 2) × 100 = 22.22%
The values differ by 20; relative to their average of 90, the difference is 22.22%.
10% moves the decimal one place left; 5% is half of 10%; 1% divides by 100. Combine these: 15% is 10% plus 5%.
Use the original value for percentage change, the whole for part-to-whole, and the average of both values for percentage difference.
A 20% discount followed by 10% off multiplies the price by 0.80 then 0.90. The combined reduction is 28%, not 30%.
A 20% fall followed by a 20% rise leaves 96% of the starting value. After falling, the same percentage acts on a smaller base.
Divide the percentage by 100, then multiply by the number. For example, 20% of 150 is 20 ÷ 100 × 150 = 30.
Percentage increase measures relative change from an original value. Percentage points measure the direct gap between two percentages; moving from 5% to 6% is 1 percentage point but a 20% increase.
Percentage change compares a new value with an original value and uses the original as the denominator. Percentage difference compares two values with no starting value and uses their average as the denominator.
Yes. A percentage over 100% means the part is larger than the whole or the value is more than the chosen reference. For example, 150 is 150% of 100.
Yes, when the values or direction make that meaningful. A negative percentage change indicates a decrease. A negative percentage of a number produces a result with the opposite sign.
Treat the sale price as the final value and choose decrease. Divide the final price by 1 minus the discount rate as a decimal. A $92 price after 20% off came from $92 ÷ 0.80 = $115.
Treat the current price as the final value and choose increase. Divide it by 1 plus the increase rate as a decimal. A $120 price after a 20% increase came from $120 ÷ 1.20 = $100.
The calculator keeps full JavaScript number precision while calculating and rounds only the displayed result to your selected number of decimal places. Choose more decimal places when intermediate precision matters.
Percentage change divides by the original value. Division by zero is undefined, so a change from zero cannot be expressed as a standard percentage change; report the absolute change instead.
