What is the percent of change from 5 to 7?

A 40% increase: (7 − 5) ÷ 5 × 100 = 2 ÷ 5 × 100 = 40%.

How do I calculate percent decrease?

The same formula; the answer just comes out negative. From 80 to 60: (60 − 80) ÷ 80 × 100 = −25%, a 25% decrease.

Why isn't a 50% drop undone by a 50% rise?

Each percentage is of a different base. 100 down 50% is 50; 50 up 50% is only 75. To get back to 100 from 50 takes a 100% increase.

What is the difference between percent change and percentage points?

Percentage points are the plain difference between two percentages; percent change is relative. From 4% to 6% is +2 points but +50%.

How do I find the new value after a percent change?

Multiply the original by 1 plus the change as a decimal. 250 up 12% is 250 × 1.12 = 280; 250 down 12% is 250 × 0.88 = 220.

How do I turn a change over several years into a yearly rate?

Use the compound annual growth rate, (new ÷ old)^(1 ÷ years) − 1. From 100 to 150 over 5 years is a 50% change in total but 1.5^(1/5) − 1 = 8.45% a year, not 10%, because each year's growth builds on the last.

Is a 100% increase the same as doubling?

Yes. A 100% increase adds the whole original again, so 50 becomes 100. Tripling is a 200% increase, and halving is a 50% decrease.

Can something fall by more than 100%?

Not a quantity that cannot go below zero: a 100% decrease leaves nothing. Rises have no such limit. A value that turns negative, such as a profit becoming a loss, can show a change beyond −100%.

Percent Change Calculator: Increase or Decrease, With Working

Percent increase or decrease from an old value to a new one, with the working and the change back.

Inputs

From (original)

-1,000,0001,000,000

To (new value)

-1,000,0001,000,000

Include CalculateEveryday mark

Percent change

38.46% increase

Before26

After36

+38.46%

Working: (36 − 26) ÷ 26 × 100 = 10 ÷ 26 × 100 = 38.4615%
Multiplier: × 1.3846
Going back: From 36 back to 26 is a 27.7778% decrease — not the same percentage, because the base has changed
From: 26
To: 36
Absolute change: 10

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What each Percent Change input means

From (original): The original or old value — the base the change is measured against. It cannot be 0. A negative starting value is divided by its size, so the direction of the change stays right.
To (new value): The new value. Anything goes, including 0 (a 100% decrease) and values more than double the original (an increase of over 100%).

Percent Change formula

percent change = (new − original) ÷ |original| × 100

\%\Delta = \frac{\text{new} - \text{original}}{|\text{original}|} \times 100

OpenStax Prealgebra sets it out in two steps: find the amount of the change (new minus original), then find what percent of the original amount that change is. A positive answer is an increase, a negative one a decrease. The base is always the original value, which is why a change and its reverse are different percentages: a rise from 26 to 36 is 38.46%, but the fall from 36 back to 26 is 27.78%, because 10 is a smaller share of 36. The page shows both, the multiplier (new ÷ original), and the working. When the original is negative — a loss, a temperature below zero — the change is divided by its size, so a move from −50 to −25 reads as an increase.

Percent Change worked example

OpenStax's own example: a fee rising from 26 to 36 a unit. The change is 36 − 26 = 10, and 10 ÷ 26 × 100 = 38.46% — a 38.5% increase. Going back down from 36 to 26 would be a 27.78% decrease, because the base is now 36.

More Percent Change examples

Rent falling from 1,200 to 900 a month: (900 − 1,200) ÷ 1,200 × 100 = −25%, which the page reports as a 25.00% decrease. Getting back from 900 to 1,200 would take a 33.33% increase, because 300 is a bigger share of 900.

A gallon of milk going from 3.49 to 3.99: the change is 0.50, and 0.50 ÷ 3.49 × 100 = 14.33% increase. The multiplier, 1.1433, is the same fact in one number: new price = old price × 1.1433.

Where the Percent Change calculator can give the wrong answer

The original value cannot be zero: any change from zero is an infinite percentage, so the page returns an error.
Percent change is not the same as percentage points. A rate going from 4% to 6% is a 2-point rise but a 50% increase.
A change and its reverse differ: down 25% from 100 is 75, and getting back to 100 needs 33.33% up.
With a negative original value the change is divided by its absolute value, so moving towards zero (−50 to −25) is an increase. Some textbooks divide by the signed value instead and call that a decrease; check which your course uses.

Spotted a mistake? Tell us

Percent Change reference table

A rise and the fall that undoes it, and the other way round
Percent	Up by this, then back down by	Down by this, then back up by
5%	4.76%	5.26%
10%	9.09%	11.11%
20%	16.67%	25%
25%	20%	33.33%
33.33%	25%	50%
50%	33.33%	100%
75%	42.86%	300%
100%	50%	— (nothing is left)

Source: Arithmetic: after a rise of p, the fall back is p ÷ (1 + p); after a fall of p, the rise back is p ÷ (1 − p)

Percent Change FAQ

: A 40% increase: (7 − 5) ÷ 5 × 100 = 2 ÷ 5 × 100 = 40%.
: The same formula; the answer just comes out negative. From 80 to 60: (60 − 80) ÷ 80 × 100 = −25%, a 25% decrease.
: Each percentage is of a different base. 100 down 50% is 50; 50 up 50% is only 75. To get back to 100 from 50 takes a 100% increase.
: Percentage points are the plain difference between two percentages; percent change is relative. From 4% to 6% is +2 points but +50%.
: Multiply the original by 1 plus the change as a decimal. 250 up 12% is 250 × 1.12 = 280; 250 down 12% is 250 × 0.88 = 220.
: Use the compound annual growth rate, (new ÷ old)^(1 ÷ years) − 1. From 100 to 150 over 5 years is a 50% change in total but 1.5^(1/5) − 1 = 8.45% a year, not 10%, because each year's growth builds on the last.
: Yes. A 100% increase adds the whole original again, so 50 becomes 100. Tripling is a 200% increase, and halving is a 50% decrease.
: Not a quantity that cannot go below zero: a 100% decrease leaves nothing. Rises have no such limit. A value that turns negative, such as a profit becoming a loss, can show a change beyond −100%.