acalculator

What is the percentage decrease?

Type the original and the new value to get the percentage decrease, or type a percent and one value to get the other.

Your numbers

Percentage decrease
20%

From 50 to 40 is a 20% decrease.

Amount of decrease
10
In words
a 20% decrease

Percentage decrease: 20%. From 50 to 40 is a 20% decrease.

How to calculate

Finds the percentage decrease from an original value to a new value, P = (V₁ − V₂) ÷ V₁ × 100, or the new or original value from the percent.

Example with the default inputs (Original value 50, New value 40): From 50 to 40 is a 20% decrease.

Formula: P = (V₁ − V₂) ÷ V₁ × 100, where V₁ is the original value and V₂ the new value.

  • The percent is taken of the original value, not of the new value.
  • The original value is greater than 0 and the new value is 0 or more, so the decrease is at most 100%.
  • A new value larger than the original gives a negative decrease, and the answer calls it an increase.
  • The original value cannot be found from a 100% decrease, because every original value falls to 0.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Original value 50, New value 40 gives Percentage decrease 20%, Amount of decrease 10, In words a 20% decrease.Source: hand calculation in content.mdx: (50 − 40) ÷ 50 × 100 = 20%
  2. Original value 3.71, New value 3.64 gives Percentage decrease 1.886792%.Source: OpenStax Prealgebra 2e, Example 6.24: a gas price from $3.71 to $3.64 is a 1.9% decrease (rounded there); (3.71 − 3.64) ÷ 3.71 × 100 = 1.8868%
  3. Original value 80, Percentage decrease 25% gives New value 60, Amount of decrease 20.Source: hand calculation in content.mdx: 80 × (1 − 0.25) = 60
  4. New value 60, Percentage decrease 25% gives Original value 80.Source: hand calculation in content.mdx: 60 ÷ (1 − 0.25) = 80
  5. Original value 40, New value 50 gives Percentage decrease -25%, Amount of decrease -10, In words a 25% increase, not a decrease.Source: hand calculation in content.mdx: (40 − 50) ÷ 40 × 100 = −25%, an increase of 25%

How it works

A percentage decrease compares the drop with the value you started from. With the original value V₁ and the new value V₂:

P = (V₁ − V₂) ÷ V₁ × 100

Type any two of the three values and the calculator finds the third:

  • the percent from the two values: P = (V₁ − V₂) ÷ V₁ × 100
  • the new value from the original and the percent: V₂ = V₁ × (1 − P ÷ 100)
  • the original from the new value and the percent: V₁ = V₂ ÷ (1 − P ÷ 100)

It also shows the amount of the decrease, V₁ − V₂.

Assumptions

  • The percent is always a percent of the original value V₁.
  • The original value is greater than 0, and the new value is 0 or more. So the decrease is at most 100%.
  • If the new value is larger than the original, the decrease is negative: that is an increase. The answer then says so in words: from 50 to 60 is "a 20% increase, not a decrease" (the percent is still (50 − 60) ÷ 50 × 100 = −20%, and the amount of decrease is −10). Equal values are "no change".
  • The answer in words ("In words") is "a P% decrease" when the new value is smaller, "a P% increase, not a decrease" with P = −(the percentage decrease) when it is larger, and "no change" when they are equal.
  • The original cannot be found from a 100% decrease (every original value falls to 0), or from a new value of 0.

Worked examples by hand

From 50 to 40. The drop is 50 − 40 = 10, and 10 ÷ 50 × 100 = 20%.

A gas price from $3.71 to $3.64 (OpenStax Example 6.24). The drop is $0.07, and 0.07 ÷ 3.71 × 100 = 1.8868%, which the textbook rounds to 1.9%.

25% off 80. 80 × (1 − 25 ÷ 100) = 80 × 0.75 = 60, a drop of 20.

60 after a 25% decrease. The original was 60 ÷ (1 − 0.25) = 60 ÷ 0.75 = 80.

From 40 to 50. (40 − 50) ÷ 40 × 100 = −25%, a drop of −10: the value rose by 25%.

Other questions people ask

How do I calculate a percentage decrease?

Subtract the new value from the original, divide by the original, and multiply by 100: (original − new) ÷ original × 100. A price that falls from $50 to $40 has dropped (50 − 40) ÷ 50 × 100 = 20%.

How do I take a percentage off a number?

Multiply by 1 minus the percent as a decimal. 25% off $80 is 80 × (1 − 0.25) = 80 × 0.75 = $60.

How do I find the original price before a discount?

Divide the sale price by 1 minus the percent as a decimal. A $60 price after 25% off was 60 ÷ 0.75 = $80. Adding 25% back to $60 gives $75, which is wrong, because the 25% was taken from $80, not from $60.

Why is a 20% fall not undone by a 20% rise?

The rise is taken from the smaller number. 50 down 20% is 40, and 40 up 20% is only 48. To get from 40 back to 50 you need a 25% rise.

What does a negative percentage decrease mean?

The value went up. From 40 to 50 is a decrease of −25%, which is an increase of 25% of the original 40.

Can a decrease be more than 100%?

Not for amounts that cannot go below zero, such as prices, weights, or counts. A 100% decrease takes the value to 0, so the calculator accepts decreases of up to 100%.

What is the difference between a percentage decrease and a percentage point decrease?

A rate that falls from 5% to 4% has dropped 1 percentage point, which is a 20% decrease of the rate: (5 − 4) ÷ 5 × 100 = 20%.