Percentage Calculator
Calculate a percentage of a number, increased and decreased values, and the relative change from an original value to a new value. All labelled results are shown together; no mode selection is needed.
On this page
Percentage of a number and percentage change: inputs and result
Enter an original number, a percentage and a new value. The main result is the entered percentage of the original. Separate results show that original increased or decreased by the percentage, plus the percentage change from original to new value.
How the calculation works
The same original number is used in all three operations. The new-value field affects the change percentage, but not the main percentage-of result. There is no mode selector or separate part/whole calculation in this form.
Formula and assumptions
Part = original × percentage ÷ 100. Increased value = original + part. Decreased value = original − part. Change percentage = (new − original) ÷ original × 100. Percentage change is undefined when the original is zero.
Using the fields
- Enter the original value.
- Enter the percentage you want to apply.
- Enter a new value only when you want the change percentage too.
- Read the labelled outputs separately; they answer different questions.
Worked examples
20% of 80
80 × 20 ÷ 100 = 16. An increase of 20% gives 96; a decrease of 20% gives 64.
Change from 80 to 100
(100 − 80) ÷ 80 × 100 = 25% increase. The reverse change is (80 − 100) ÷ 100 × 100 = −20%, because the original value changes.
Percentage points
A rate moving from 10% to 12% rises by 2 percentage points, or 20% relative to the original rate.
Reading the result
Use the main result for a share of a number. Use the change result for before-and-after comparisons. A negative change means a decrease from a positive original value.
Common mistakes
- Confusing a percentage-point difference with a relative change.
- Using the new value as the denominator for change.
- Adding successive discounts instead of applying each to the reduced price.
What is included
This is arithmetic on the values entered. It does not determine whether a price, growth rate or performance change is desirable. Keep the same unit and time period in a before-and-after comparison.
Supporting guides for this calculator
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Frequently asked questions
Why does the main result not change when I edit the new value?
The main result is original×percentage÷100. The new value is used only for the labelled change-percentage result.
Why is an increase of 25% reversed by a 20% decrease?
The two percentages use different original values. Moving 80→100 adds 20 relative to 80; moving 100→80 removes 20 relative to 100.
Can I calculate change from zero?
Relative percentage change from zero has no finite value because it requires division by zero. Report the absolute change instead.
Comparing two product prices?
Percentage difference shows how far apart two prices are. When pack sizes differ, use the unit price calculator for a like-for-like comparison before deciding which product is cheaper.
Using this calculation
Choose the labelled output that matches the question: a percentage of the original, an increased or decreased value, or the relative change to a new value.