Skip to main content
Bethemesh
Mathematics & calculation

Percentage decrease calculator

Calculate the percentage decrease between two values, take X% off a price, a usage figure or a budget, or find the original value before a decrease. Formulas, multiplier and why a decrease and an increase do not cancel out, with examples.

Embed this widget

Customize the result, check the live preview, then copy the code.

Preview

Embed code type

Code to copy

Responsive and automatically resized by Bethemesh.

Change

-

Was this tool useful?

How does this tool work?

This page handles the three calculations around a decrease: the percentage decrease between two values, the value left after an X% decrease, and the original value when you only know the result after the decrease. It applies to price cuts, lower energy use, weight loss, headcount, spending or revenue drops, and to percentage change exercises.

Rate of decrease between two values: t = (final value − starting value) ÷ starting value × 100. The result is negative for a decrease: a bill that goes from $150 to $120 changes by −30 ÷ 150 = −20%. In other words, it decreased by 20%.

Decreasing a value by X%: multiply it by the factor 1 − X ÷ 100. Cutting by 15% means multiplying by 0.85; cutting by 40% by 0.6. Energy use of 4,800 kWh reduced by 15% drops to 4,800 × 0.85 = 4,080 kWh.

Finding the value before the decrease: divide the final value by the same factor. A product selling for $68 after a 15% cut was 68 ÷ 0.85 = $80. Adding 15% to $68 would give $78.20: that is the most common mistake. A 100% decrease brings the value to zero and the original value cannot be recovered; in that case the tool shows no result.

A decrease and an increase do not cancel out. After a 20% decrease, you need a 25% increase to get back to the start, because the increase applies to a smaller base. More generally, a t% decrease is offset by an increase of t ÷ (1 − t).

How to use this tool

  1. Choose your question

    % change, Decrease by X% or Value before decrease.

  2. Enter the two numbers

    Prices, quantities, durations or index values, in the same unit.

  3. Read the result

    The rate is shown with its sign (negative for a decrease) or the calculated value, rounded to two decimal places.

Percentage decrease formulas

Three calculations linked by the multiplier k = 1 − t ÷ 100.

Rate of change

t = (VA − VD) ÷ VD × 100

Negative when the value decreases.

Value after a t% decrease

VA = VD × (1 − t ÷ 100)

Multiply by a factor below 1.

Value before the decrease

VD = VA ÷ (1 − t ÷ 100)

Reverse percentage, defined for a decrease below 100%.

Increase that offsets a decrease

t' = t ÷ (100 − t) × 100

For t = 20%, you need t' = 25%.

VD
starting (original) value, the reference
VA
final value
t
rate of decrease, in %
t'
increase needed to get back to the starting value

Example: a 35% decrease means k = 0.65; 400 becomes 260.

Use cases

Shopping and prices

Measure the real drop in a price between two dates or two stores, and find the original price of an item already marked down.

Energy and budget

Set a percentage target for cutting energy use or spending and turn it into kWh, gallons or dollars.

Business metrics

Quantify a drop in revenue, traffic, unemployment rate or inventory between two periods.

Math exercises

Review the multiplier for a decrease, successive changes and reverse percentages.

Examples

Lower bill

(120 − 150) ÷ 150 × 100 = −20%.

Input

from $150 to $120

Result

−20%

Reduction target

4,800 × 0.85 = 4,080 kWh, saving 720 kWh.

Input

4,800 kWh − 15%

Result

4,080 kWh

Price before the cut

68 ÷ 0.85 = $80.

Input

$68 after −15%

Result

$80

Weight loss

6.8 kg lost compared with the starting 85 kg.

Input

from 85 kg to 78.2 kg

Result

−8%

Decrease then increase

100 × 0.8 × 1.2 = 96: still 4% short of the start.

Input

100 − 20% then + 20%

Result

96

Tips and best practices

  • Always divide by the starting value: from 150 to 120 is −20%; from 120 to 150 is +25%.
  • To undo a decrease, divide by (1 − t): do not add the same percentage back.
  • Two successive 10% decreases make −19% in total (0.9 × 0.9 = 0.81), not −20%.
  • A decrease cannot exceed 100% for a positive quantity: beyond that, the value would become negative.
  • For a store discount with a crossed-out price or stacked discounts, the discount calculator also shows how much you save.

Sources and references

Frequently asked questions

How do I calculate a percentage decrease?

Calculate (final value − starting value) ÷ starting value × 100. From 250 to 200: (200 − 250) ÷ 250 × 100 = −20%, a 20% decrease.

How do I take 30% off a price?

Multiply it by 0.70. A $59 item with 30% off costs $41.30. A 25% decrease means × 0.75 and a 10% decrease means × 0.9.

How do I find the value before a decrease?

Divide the final value by 1 − the rate. If take-home pay dropped to $1,840 after an 8% cut, it was 1,840 ÷ 0.92 = $2,000.

Why isn't a 20% decrease offset by a 20% increase?

The increase applies to the value that has already been reduced. 100 minus 20% gives 80, and 80 plus 20% gives 96. You need a 25% increase to get back to 100.

What is the difference between a percentage decrease and a drop in points?

A rate that goes from 10% to 8% falls by 2 percentage points, but by 20% in relative terms (2 ÷ 10). Both statements are correct, but they do not say the same thing.

Can the result go below −100%?

Not for a positive quantity that stays positive: −100% means the value has fallen to zero. A lower result only occurs when the final value turns negative, such as a profit turning into a loss.

Related tools

Keep going with these tools

Tools similar or complementary to this one.

Similar tools

Percentage increase calculator

Find the percentage increase between two values, add X% to a value or work back to the value before the increase.

Mathematics & calculationUse this tool

Read next