Percentage Calculator
Solve the five common percentage questions: X% of Y, X as a percent of Y, increase, decrease, and the whole from a part.
Calculation Type
Quick Examples
Common Percentage Calculations:
Tips: Usually 15-20% of bill
Sales Tax: Varies by location (0-10%)
Discounts: Often 10%, 25%, 50% off
Interest Rates: Annual percentage rates
Grades: Score/Total × 100
Growth: (New-Old)/Old × 100
Updated Formula covered by automated tests
Almost every percentage question is one of five shapes: what is X percent of Y, what percent of Y is X, how much did something rise, how much did it fall, and what was the whole if a known part is a given share of it. This page puts all five behind one set of inputs. Pick the question, type the two numbers, and the result appears with the formula that produced it, so you can check the logic rather than trust a black box.
Typical uses are grading a test out of an odd total, working out what share of take-home pay goes to rent, reading a news story that says prices rose 3.4 percent, or reverse-engineering the full amount from a partial figure such as a 25 percent deposit. If you need to apply two changes one after another (a raise followed by another raise, or a markdown on top of a markdown), use the double percentage calculator instead, because those changes do not simply add.
The formula
- X, Y
- The two numbers you enter; which one is the part and which the whole depends on the question selected
- old
- The starting or reference value for a change (must not be zero)
- new
- The value after the change
- part, percent
- A known portion and the share of the total it represents
Per cent comes from the Latin per centum, "for each hundred". A percentage is a fraction whose denominator has been fixed at 100, which is why every formula above either divides by 100 to turn a percentage into a plain multiplier or multiplies by 100 to turn a ratio into a percentage.
Percent change always divides by the old value, and that choice of base is the source of most confusion. Going from 80 to 100 is a 25 percent increase because the 20-unit gap is measured against 80, while going back from 100 to 80 is a 20 percent decrease because the same gap is now measured against 100.
Worked example
Lena earns $4,000 a month after tax. Her landlord raises the rent from $1,250 to $1,340, and she wants to describe the change accurately when she talks to her roommate.
- 1 Percent increase in rent: (1,340 − 1,250) ÷ 1,250 × 100 = 90 ÷ 1,250 × 100 = 7.2%.
- 2 Share of income before: 1,250 ÷ 4,000 × 100 = 31.25%.
- 3 Share of income after: 1,340 ÷ 4,000 × 100 = 33.5%.
- 4 Change in share: 33.5 − 31.25 = 2.25 percentage points.
- 5 Check with the "find the whole" mode: if $1,340 is 33.5% of her pay, the whole is 1,340 × 100 ÷ 33.5 = $4,000.
Result: The rent went up 7.2%, and its share of Lena’s income went from 31.25% to 33.5%, a rise of 2.25 percentage points (not 2.25%).
Before you rely on the result
- Results are rounded to two decimal places for display; carry more precision yourself if the figure feeds into a further calculation.
- Percent change is undefined when the starting value is zero, and it gives misleading answers when the start and end have opposite signs (for example a loss turning into a profit).
Frequently asked questions
What is the difference between a percent and a percentage point?
A percentage point is the plain difference between two percentages, while a percent change is measured relative to the starting percentage. If a savings rate moves from 4% to 5%, that is 1 percentage point, but it is a 25% increase in the rate. News reports on interest rates and polls usually mean points.
Can a percentage decrease be more than 100 percent?
A decrease of exactly 100% takes any positive amount to zero, so a positive price cannot fall further. Increases have no ceiling: doubling is +100%, tripling is +200%. A result above 100% in the decrease mode means the new value has gone negative, which makes sense for profits or temperatures but not for prices.
Is X percent of Y the same as Y percent of X?
Yes. Both equal X × Y ÷ 100, so 8% of 50 and 50% of 8 are both 4. This is a handy mental-math trick: 4% of 75 is hard, but 75% of 4 is obviously 3.
How do I find a percentage of a test score out of an odd total?
Choose "What Percentage" and enter your points as the first value and the maximum as the second. For 47 out of 62, 47 ÷ 62 × 100 = 75.81%. Round only at the end, because rounding the ratio first (0.76) would report 76%.