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Miraç Özdemir
Percentages & Change

Percentage and Change Calculator

Calculate a percentage of a number, the ratio and percent change between two numbers, increase or decrease a number by a percentage, and work backwards to the whole.

Version 3

Things to keep in mind:

  • A percentage point change is not the same as a percent change: moving from 10 % to 12 % is 2 points but a 20 % relative increase.
  • A cannot be zero; a percentage change from zero is undefined.
  • Increasing a number by p % and then decreasing it by p % does not return the original value.
  • The tool does not apply VAT, interest or tax rules; use the dedicated calculators for those.

Calculator

Numbers and rate

The value to take a percentage of, to increase/decrease, or the starting value in a comparison. Must be greater than zero; any unit works (pieces, kg, currency…).

The second value compared with A (for ratio and change). May be negative.

Enter 12.5 for 12.5 %. Values above 100 % (e.g. a 150 % increase) are allowed; a negative rate reverses the direction. Minimum is -100.

After the first calculation, the result updates automatically when you change a value.

Result

Enter the values and press Calculate to see the result here.

About this tool

This calculator handles the percentage operations needed every day in one place. A is the base number, B the comparison number and p the percentage rate.

Formulas

  • p % of A = A × p / 100
  • B as a percentage of A = B / A × 100
  • Percent change from A to B = (B − A) / A × 100 (negative means a decrease)
  • Increase A by p % = A × (1 + p/100); decrease = A × (1 − p/100)
  • Symmetric percentage difference = |A − B| / ((A + B) / 2) × 100
  • If A is p % of a whole, whole = A × 100 / p
  • If A is a value already increased by p %, original = A / (1 + p/100)

Example: with A = 200, B = 250, p = 10: 10 % of 200 is 20.00; 250 is 125 % of 200; the change is a 25 % increase; 200 increased by 10 % gives 220.00 and decreased by 10 % gives 180.00. The percentage difference is 50 / 225 × 100 = 22.22 %.

The rate may exceed 100 % (a 150 % increase means 2.5 times the value). Results are rounded half-up to two decimals. The tool does pure number arithmetic with no unit or currency assumption.

How to use

  1. Enter the base number (A).
  2. Enter the second number (B) if you want a comparison.
  3. Enter the percentage rate (12.5 for 12.5 %).
  4. Press Calculate and read the result you need.

Notes

Results are rounded half-up to two decimals. Percent change uses A as the reference, so A cannot be zero. The percentage difference uses the mean of both values, so it differs from percent change. If a decrease exceeds 100 % the result is shown as 0.

Frequently asked questions

5 questions

  1. New value = old value × (1 + rate/100). For example a 10 % increase on 200 is 200 × 1.10 = 220. For the increase between two numbers use (B − A) / A × 100.

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