Step 1
Convert the percentage to a decimal.
Calculation Sheet / 01
Percentage Calculator
Calculate percentages, compare values, and see the formulas behind each answer. Enter your numbers to get a clear result instantly.
What is P% of N?
Rounding applies only to the displayed figures. Intermediate arithmetic uses JavaScript Number, which is not arbitrary-precision decimal arithmetic. Very large values can lose precision.
Calculated Result
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See How the Answer Is Calculated
Step 2
Multiply by the base number.
Step 3
Display the result.
Choose a Percentage Calculation
Dedicated pages: percentage of a number · what percent is · percentage change · increase or decrease · reverse · discount · difference
What Percentage Is One Number of Another?
What percent is A of B? Formula: Percentage = (Part / Total) × 100. A zero total cannot be used as a denominator. Results above 100% are allowed. Opposite signs can produce a negative percentage.
Percentage
Part value
Total value
Formula
Calculation
Percentage Change Calculator
This tool compares an original value with a new value. Percentage Change = ((New − Original) / Original) × 100. The original must be greater than zero. The new value must be zero or greater. This version is for nonnegative quantities with a positive baseline. Absolute change is New − Original and is not the same figure as the percentage.
Percentage change
Absolute change
Formula
Calculation
Absolute formula
Swapping 80 and 100 turns a 25% increase into a 20% decrease. The rates are not symmetric.
Increase or Decrease a Number by a Percentage
Increase: Starting × (1 + Rate / 100). Decrease: Starting × (1 − Rate / 100). Starting value must be zero or positive. Increase rates are 0–1000%. Decrease rates are 0–100%. A 100% decrease produces zero.
Original value
Percentage change amount
Final value
Formula
Calculation
Reverse Percentage Calculator
Three modes recover an original value. Verification applies the matching forward formula and checks the entered final value within relative tolerance 1e-8. A failed check is reported; a passed check is not invented.
Original value
Final value
Rate
Formula
Calculation
Discount Calculator
Discounts are applied sequentially. A 20% discount then 10% is not a 30% discount. Optional tax is calculated after discounts. Currency symbols format the display only; they do not convert amounts. This is not a location-specific tax engine. Checkout totals may differ because of retailer rounding.
Original price
First discount amount
Second discount amount
Total savings before tax
Price after discounts
Optional tax
Final price
Percentage Difference Between Two Numbers
This is not percentage change. Percentage Difference = |A − B| / ((|A| + |B|) / 2) × 100. The measure is symmetric. If A and B are both zero, the tool reports 0% under a documented identical-zero convention. One zero and one nonzero value yield 200%.
Percentage difference
Absolute difference
Average magnitude
Formula
Calculation
See the Percentage
A 10 × 10 grid of 100 squares. This diagram is for 0–100% only. Fractional percentages fill part of the next square and are described as a fraction of 100, not as a rounded whole number of squares.
35% of 100
Common Percentage Questions
The same ten rows also live on the worked examples page with the matching calculators underneath.
Percentage Formulas Explained
1. Percentage of a number
Readable: the result is the percentage divided by 100, then multiplied by the number. Example: 15% of 200 is 30. Edge case: 0% of any finite N is 0. Open calculator
2. What percent one value is of another
Readable: divide the part by the total, then multiply by 100. Example: 25 of 200 is 12.5%. Edge case: B = 0 is undefined. Open calculator
3. Percentage change
Readable: subtract original from new, divide by original, multiply by 100. Example: 80 to 100 is a 25% increase. Edge case: original 0 is undefined. Open calculator
4. Percentage increase and decrease
Readable: multiply by one plus the rate to increase, or one minus the rate to decrease. Example: 150 increased by 20% is 180. Edge case: a 100% decrease is 0. Open calculator
5. Reverse percentage
Readable: divide the later value by the same multiplier the forward step used. Example: 125 after a 25% increase came from 100. Edge case: 100% decrease cannot uniquely recover an original. Open calculator
6. Discount calculation
Readable: apply each discount to the remaining price. Example: 20% then 10% of 100 is 72, not 70. Edge case: 100% first discount leaves 0. Open calculator
7. Percentage difference
Readable: absolute difference divided by average magnitude, times 100. Example: 40 and 60 differ by 40%. Edge case: 0 and 0 is treated as 0% by convention. Open calculator
Common Percentage Mistakes
01 — Dividing by Zero
A percentage of a total, or a change from an original, needs a nonzero denominator.
Incorrect: 10 / 0 × 100 = infinity.
Correct: refuse the calculation and say it is undefined. Example: “what percent is 5 of 0?” has no percentage. What percent calculator
02 — Confusing Percent With Percentage Points
A rate that moves from 20% to 25% rose 5 percentage points. The relative increase is (25 − 20) / 20 × 100 = 25%.
Incorrect: calling both “a 5% increase.”
Correct: name the unit. Five percentage points is not a 5% relative change from 20%. Percentage change
03 — Adding Consecutive Discounts
20% then 10% off 100 is 72, because the second 10% applies to 80.
Incorrect: 20 + 10 = 30% off, leaving 70.
Correct: multiply sequential remaining factors. Discount calculator
04 — Reversing a Percentage Increase Incorrectly
A 20% increase from 100 is 120. Subtracting 20% of 120 gives 96, not 100.
Incorrect: 120 × 0.80 = original.
Correct: 120 / 1.20 = 100. Reverse calculator
05 — Treating Percent Change as Symmetric
80 to 100 is +25%. 100 to 80 is −20%.
Incorrect: assuming the reverse trip uses the same 25%.
Correct: the denominator is whichever value is original for that question. Change calculator
06 — Rounding Too Early
This site rounds only for display. Intermediate factors keep full available Number precision.
Incorrect: rounding 1/3 to 0.33 then multiplying a large base.
Correct: compute first, then round the shown result. Main calculator
07 — Assuming Percentages Cannot Exceed 100
150 is 150% of 100. Parts can exceed totals.
Incorrect: capping every ratio at 100%.
Correct: report 150% when the arithmetic says so. What percent
08 — Confusing Percentage Difference With Percentage Change
40 to 60 is a 50% increase (change) and a 40% difference (symmetric).
Incorrect: using one name for both.
Correct: use change when there is a starting point; use difference when the values are peers. Difference calculator
About and Contact
Percent Folio is an independent collection of browser-based percentage calculators and educational guides. Calculations stay in this browser. They are not financial or tax advice.
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