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Mathematics · Percentages

Calculate a percent decrease from A to B

Enter an original amount and a smaller later amount. The result is the drop relative to the original — the same idea as a markdown, without applying a sale price formula.

Calculate

Value before the drop. Zero is not allowed (denominator).

Value after the drop, less than or equal to the original. A rise is rejected here.

How the calculator works

The engine takes the absolute gap, divides by the absolute original, and multiplies by 100. A final value above the original is refused so this page stays a decrease tool. Zero as the original is refused. Going all the way to zero is a 100% decrease.

Formula and method

baisse = |final − initial| ÷ |initial| × 100

From 100 to 80: |−20| ÷ 100 × 100 = 20%. The percent is reported as a positive decrease.

Decrease mode requires final ≤ original. The display shows the percent drop and the raw gap. This is not the sale-price page: a 20% decrease from 100 to 80 matches a 20% discount on 100, but stacked discounts multiply and live on the discount calculator.

Worked example

From 100 to 80

original = 100, final = 80

  1. Gap: 100 − 80 = 20.
  2. 20 ÷ 100 = 0.20.
  3. × 100 → 20%.

A 20% decrease.

From 250 to 200

original = 250, final = 200

  1. Gap 50.
  2. 50 ÷ 250 = 0.20 → 20%.

Also 20%, even though the raw gap (50) is larger than in the 100-to-80 case.

Input notes

Original amount
The starting amount. A small original makes a modest raw drop look large in percent terms.
Final amount
The later amount. Must be ≤ original. For a rise, use percent increase.

Assumptions and limits

Assumptions

  • Same quantity, later smaller (or equal).
  • The base is the original, not the final value.

Limits

  • Does not apply a discount to a list price (see the discount calculator).
  • Does not annualize a month-to-month drop.

How to read the result

A 20% decrease means one fifth of the original is gone. Recovering 80 back to 100 is a 25% increase, not 20%. For a posted sale (“20% off”), the discount tool starts from list price instead of from two observed amounts.

Common mistakes

  • Dividing the gap by the final amount (20/80 = 25%).

    A decrease is relative to what you had. From 100 to 80 the base is 100, so 20%.

  • Treating a 20% fall as the inverse of a 20% rise.

    They use different bases. 100 → 80 is −20%; 80 → 100 is +25%.

Methodology · Sources

Related calculations

Frequently asked questions

Is a decrease to zero a 100% drop?

Yes, if the original is not zero.

|0 − original| / |original| = 1, so 100%. The original still cannot be zero, because that would be 0/0.

How is this different from a discount calculator?

Here you already know both amounts. A discount starts from list price and a percent off.

If you watched a price move from $100 to $80, this page names the drop. If a tag says 20% off $100, the discount page returns $80. Stacked percents off are not added; they multiply, which the discount page explains.

Can I enter a negative original?

Yes, as long as it is not zero; the formula uses absolute values.

A move from −40 to −50 is a decrease in the signed sense the engine enforces (final ≤ original). The percent uses |original| in the denominator. Read signed series with extra care.

Author and update

Written by Rédaction HexaCalc (editorial team). Content last updated: August 25, 2026. No third-party medical or financial review is claimed.

This calculation uses a standard mathematical identity. See also the methodology.

Price off a list amount

If you have a sticker price and a percent off, compute the sale price directly instead of typing both observed amounts.

Open the discount calculator

Category: Mathematics