NumberUtils

Percentage Decrease Calculator

Enter a starting value and a percentage to find what the value becomes after decreasing it by that percentage.

One multiplication covers a sale reduction, a price cut, or any figure reduced by a set proportion. If you are not sure which direction the calculation runs, the Percentage Calculator covers increases, decreases and reversing a known change in one place.

Result

80

New value = original × (1 − percentage ÷ 100)

How it works

The original value is multiplied by 1 minus the percentage expressed as a decimal, so a 20% decrease multiplies by 0.80.

Taking 15% off 240: divide 15 by 100 to get 0.15; take that off 1 to get 0.85, the share of the original that remains; multiply 240 by 0.85 to get 204. The amount removed is the difference between the two figures, 240 − 204 = 36.

A decrease and an increase of the same size do not cancel out, because each step works from whatever value came before it: 200 decreased by 50% is 100, and increasing that 100 by 50% gives 150, not 200. The Percentage Increase Calculator runs the opposite calculation.

Formula: New value = original × (1 − percentage ÷ 100)

Examples

A discounted price

100 decreased by 20% is 100 × 0.80 = 80.

A larger decrease

50 decreased by 40% is 50 × 0.60 = 30.

A percentage with a decimal

2,400 decreased by 8.5% is 2,400 × 0.915 = 2,196, a saving of 204.

A result with three decimal places

450 decreased by 14.99% is 450 × 0.8501 = 382.545, a saving of 67.455.

Common uses

  • Working out what an item costs during a sale advertised as a percentage reduction
  • Applying a planned reduction to a budget or a spending target
  • Turning a reported fall such as "down 4% on last year" into an amount for a given figure

Things to keep in mind

  • This calculator finds the value after a decrease. To go the other way — working out what a value was before a known decrease — use the reverse-percentage mode on the main Percentage Calculator instead.
  • A percentage decrease of 100% or more always gives zero or a negative result, since decreasing a value by 100% removes all of it. This is a correct, if unusual, answer rather than an error.
  • A negative percentage is not rejected: entering −10 gives the same answer as a 10% increase, so a mistyped sign turns the decrease into an increase instead of stopping the calculation.
  • This calculator takes one value and one percentage. To express the same fall as a signed change against a starting figure, use the Percentage Change Calculator.
  • The result is tidied to 12 significant digits and displayed with up to 10 decimal places, so a figure that would otherwise repeat is shown rounded rather than as an endless string of digits.

Frequently asked questions

How do I decrease a number by a percentage?

Multiply the number by 1 minus the percentage divided by 100. For a 20% decrease on 100, multiply 100 by 0.80 to get 80.

What happens if I enter a decrease of more than 100%?

The result goes negative, which is mathematically correct: decreasing 100 by 150%, for example, gives −50.

How do I work out how much a percentage decrease saves?

Subtract the new figure from the original: 240 decreased by 15% is 204, so the saving is 240 − 204 = 36. The Discount Calculator reports the saving alongside the sale price.

Background and method

  • Percentages The five everyday percentage calculations, percentage points versus percent, successive changes, and why reversing a percentage is not the same as applying it backwards.
  • Methodology: Percentages The exact rules, input limits and rounding this calculator follows.
Percentage Increase Calculator Find the new value after increasing a number by a percentage. Percentage Change Calculator Find the percentage change between an original value and a new value. Percentage Calculator Find a percentage of a number, work out percentage change, or reverse a percentage back to its original value.