Percent Change Calculator
Find the percent increase or decrease from an old value to a new one with the working shown, or apply a percent change, undo one to find the original, chain several changes and get the average rate per period.
How it works
Percent change = (New − Old) ÷ |Old| × 100 · New = Old × (1 + p ÷ 100) · Old = New ÷ (1 + p ÷ 100) · Chained changes: multiplier = (1 + p₁ ÷ 100) × (1 + p₂ ÷ 100) × … · Average rate over n periods = (New ÷ Old)^(1/n) − 1
Percent change measures how much a value grew or shrank relative to where it started. Subtract the old value from the new one, divide by the absolute value of the old value, and multiply by 100. A positive answer is an increase and a negative answer is a decrease. Dividing by the absolute value keeps the sign honest when the starting value is below zero. The calculation has no answer when the original value is zero. The same idea also works in reverse. A change of p% multiplies a value by (1 + p ÷ 100), so you can apply a change to get the new value or divide by the multiplier to recover the original. Several changes in a row multiply rather than add, which is why +10% followed by −10% leaves you 1% below where you started. Under More options you can give the number of periods between the values to get the average compound rate per period. You can also mark the values as percentages to see the change in percentage points, and fix the rounding.
Worked example
Going from 80 to 100, the difference is 100 − 80 = 20. Divided by the original 80 that is 0.25, or a 25% increase. To get back from 100 to 80 needs a 20% decrease, because the base is now 100. If the rise took 2 years, the compound rate is (100 ÷ 80)^(1/2) − 1 ≈ 11.8% a year. Applying +10%, −5% and +20% in a row to 80 multiplies it by 1.1 × 0.95 × 1.2 = 1.254, giving 100.32. That is an overall change of +25.4%, not the +25% you get by adding the percentages.
Sources: Relative change — Wikipedia
Frequently asked questions
What is the difference between percent change and percentage points?
Percent change is relative to the starting value, while percentage points are a plain subtraction of two percentages. A rate going from 20% to 25% rose by 5 percentage points but by 25% in percent-change terms. Switch on “The values are percentages” to see both.
Why does a 20% drop not undo a 20% rise?
Each percent is taken of a different base. 100 up 20% is 120, but 20% of 120 is 24, so dropping 20% lands on 96. To undo a 20% rise you need a decrease of 20 ÷ 120 ≈ 16.67%. The calculator shows this as the change needed to get back to the original.
How do I find the original price before a percent increase?
Divide by the multiplier rather than subtracting the percent. If a price is 138 after a 15% rise, the original is 138 ÷ 1.15 = 120. Taking 15% off 138 gives 117.30, which is too low. Choose “Original value before a percent change” to do this.
What if the original value is negative?
The difference is divided by the absolute value of the original, so the sign of the answer matches the direction of the move. Going from −10 to −25 is a −150% change because the value fell. When the two values have opposite signs the percentage can look extreme, so the absolute change is often the clearer figure.
How do I combine several percent changes?
Turn each one into a multiplier (1 + p ÷ 100) and multiply them together. +10%, −5% and +20% give 1.1 × 0.95 × 1.2 = 1.254, an overall change of +25.4%. Choose “Several percent changes in a row” and list them separated by commas.
What is the average percent change per year?
When a value moves from Old to New over n periods, the steady rate that gets you there is (New ÷ Old)^(1/n) − 1, the compound annual growth rate. Dividing the total percent change by n gives the simple average, which overstates growth because it ignores compounding.
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This calculator is for educational purposes. Double-check important results before acting on them.