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Percentage Calculator

Solve 12 percentage tasks with transparent formulas, steps, validation, and exact versioning.

12 calculation modes

Calculate a percentage

What is p% of x?

Result

Enter values and choose Calculate.

Formula version 1.0.0 · Inputs stay in this browser.

Transparent methods

Percentage formulas

Choose the formula that matches the relationship in your question. The calculator keeps full working precision and rounds only the displayed result.

Percentage of a value

r = (p ÷ 100) × x

Convert the percentage to a decimal, then multiply by the value.

Domain: p and x may be any finite numbers.

One value as a percentage of another

r = (x ÷ y) × 100

Divide the part by the whole, then convert the ratio to a percentage.

Domain: The whole y must not be zero.

Percentage change

r = ((b − a) ÷ |a|) × 100

Compare the signed change with the magnitude of the original value.

Domain: The original value a must not be zero.

Increase by a percentage

r = x × (1 + p ÷ 100)

Add the percentage rate to the original multiplier of 1.

Domain: Negative p behaves like a decrease.

Decrease by a percentage

r = x × (1 − p ÷ 100)

Subtract the percentage rate from the original multiplier of 1.

Domain: A decrease above 100% crosses zero and produces a negative result.

Percentage difference

r = |a − b| ÷ ((a + b) ÷ 2) × 100

Compare the absolute difference with the arithmetic mean when neither value is the reference.

Domain: a and b must be nonnegative and cannot both be zero.

Original before an increase

x = y ÷ (1 + p ÷ 100)

Undo the increase by dividing the final value by its multiplier.

Domain: p must not equal −100%.

Original before a decrease

x = y ÷ (1 − p ÷ 100)

Undo the decrease by dividing the final value by its multiplier.

Domain: p must not equal 100%.

Fraction to percentage

r = (n ÷ d) × 100

Divide the numerator by the denominator and multiply by 100.

Domain: The denominator d must not be zero.

Decimal to percentage

r = x × 100

A decimal becomes a percentage when multiplied by 100.

Domain: x may be any finite decimal.

Percentage to decimal

r = p ÷ 100

A percentage becomes a decimal when divided by 100.

Domain: p may be any finite percentage.

Percentage to fraction

p% = i ÷ (100 × s)

Represent the typed percentage as integer i over decimal scale s, then reduce numerator and denominator by their greatest common divisor.

Domain: The typed percentage may contain at most 12 decimal places and must remain within safe-integer limits.

Symbol definitions

p
The percentage rate written without the percent sign; for example, 20 means 20%.
x
A value, starting value, part, decimal, or recovered original as identified by the selected mode.
y
The comparison whole or the final value in a reverse-percentage calculation.
a
The original value for change, or the first value for difference.
b
The new value for change, or the second value for difference.
n
The numerator of a fraction.
d
The denominator of a fraction; it cannot be zero.
i
The exact integer digits parsed from a terminating percentage.
s
The power-of-ten scale matching the typed decimal places.
r
The raw, unrounded calculation result.
|a|
The absolute magnitude of a; it is nonnegative.

Step-by-step practice

Worked percentage examples

These original examples cover every calculation mode. Follow the substitution and arithmetic, then compare the result with the answer.

Example 1

Find 15% of 240

A workshop has 240 seats. How many seats are 15% of the total?

  1. 15 ÷ 100 = 0.15
  2. 0.15 × 240 = 36

Answer: 15% of 240 is 36 seats.

Example 2

Find what percent 42 is of 168

A reader finished 42 pages of a 168-page section. What percentage is complete?

  1. 42 ÷ 168 = 0.25
  2. 0.25 × 100 = 25%

Answer: 42 is 25% of 168.

Example 3

Measure a directed increase

A weekly total rises from 64 to 80. What is the percentage change?

  1. 80 − 64 = 16
  2. (16 ÷ |64|) × 100 = 25%

Answer: The percentage change is +25%.

The original value, 64, is the reference, so direction matters.

Example 4

Increase 72 by 12.5%

A course adds 12.5% more practice questions to a set of 72. What is the new total?

  1. 1 + (12.5 ÷ 100) = 1.125
  2. 72 × 1.125 = 81

Answer: The increased total is 81 questions.

Example 5

Decrease 250 by 18%

A 250-unit allocation is reduced by 18%. How many units remain?

  1. 1 − (18 ÷ 100) = 0.82
  2. 250 × 0.82 = 205

Answer: 205 units remain.

Example 6

Compare 84 and 96 equally

Two equal-status samples measure 84 and 96. What is their percentage difference?

  1. |84 − 96| = 12
  2. (84 + 96) ÷ 2 = 90
  3. (12 ÷ 90) × 100 = 13.333…%

Answer: The percentage difference is about 13.33%.

Neither value is the reference; swapping them gives the same answer.

Example 7

Recover a value before a 15% increase

A total is 138 after a 15% increase. What was the original total?

  1. 1 + (15 ÷ 100) = 1.15
  2. 138 ÷ 1.15 = 120

Answer: The original total was 120.

Example 8

Recover a value before a 15% decrease

A total is 153 after a 15% decrease. What was the original total?

  1. 1 − (15 ÷ 100) = 0.85
  2. 153 ÷ 0.85 = 180

Answer: The original total was 180.

Example 9

Convert 7/8 to a percentage

Seven of eight checkpoints are complete. What percentage is that?

  1. 7 ÷ 8 = 0.875
  2. 0.875 × 100 = 87.5%

Answer: 7/8 equals 87.5%.

Example 10

Convert 0.375 to a percentage

Write the decimal 0.375 as a percentage.

  1. 0.375 × 100 = 37.5

Answer: 0.375 equals 37.5%.

Example 11

Convert 62.5% to a decimal

Write 62.5% as a decimal.

  1. 62.5 ÷ 100 = 0.625

Answer: 62.5% equals 0.625.

Example 12

Convert 37.5% to a fraction

Write the terminating percentage 37.5% as a reduced fraction.

  1. 37.5% = 375/1000
  2. 375/1000 ÷ 125/125 = 3/8

Answer: 37.5% equals 3/8.

Rounding note: Repeating decimals are shown with an ellipsis during the working and rounded in the written answer. The calculator keeps its full numeric result until display.

How to use this calculator

  1. Choose the calculation type that matches your question.
  2. Enter the values shown for that calculation type, using a percentage without the percent sign where requested.
  3. Select Calculate.
  4. Read the labeled result, warning when present, and open Calculation steps to check the substitution and arithmetic.

Assumptions, rounding, and limits

  • The calculator accepts finite numbers and applies each mode's displayed domain restrictions.
  • It keeps working precision through the calculation and rounds only the displayed result.
  • Percentage change uses the original value as reference; percentage difference treats two nonnegative values symmetrically.
  • Percentage-to-fraction conversion accepts at most 12 decimal places and uses exact decimal text within safe-integer bounds.

Frequently asked questions

Is percentage change the same as percentage difference?

No. Change compares a new value with a defined original and can be negative. Difference compares two nonnegative values without choosing an original and is nonnegative.

Can a percentage be greater than 100 or negative?

Yes when the selected formula remains defined. A decrease above 100% crosses zero, so the calculator displays a warning.

Why can reversing a percentage give a different number?

A percentage increase or decrease is based on its starting value. Reverse modes divide by the original multiplier instead of applying the opposite percentage.

Sources and review

Formula version
percentage.general@1.0.0
Formula review
Equatara formula review
Editorial review
Equatara editorial review
Last verified
2026-10-25
Applicability
Global, stable mathematics; no jurisdiction or effective-year dependency.
Next review
On material formula/source change, or by 2028-10-25.

Found a problem?

Report a formula, result, example, source, or accessibility issue through the calculator correction process. Do not include sensitive input values.