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Percentage point calculator

Compare two percentages in percentage points and relative change, or recover a missing rate. Optionally translate the gap to amounts on a shared total.

Calculator

Starting percentage
20.00000000%
Ending percentage
25.00000000%
Signed percentage point change
5.00000000
Relative change from starting rate
25.00000000%
Amount at starting rate
40.00000000
Amount at ending rate
50.00000000
Amount difference
10.00000000

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How this calculator works

A percentage point is one unit on the 0 to 100 percentage scale. Subtract the starting percentage from the ending percentage to get the signed gap. Relative change divides that gap by the starting rate and answers a different question. Amount comparisons assume both rates apply to exactly the same total.

Formula

Point change = 100(p₂ - p₁). Relative change = (p₂ - p₁)/p₁ when p₁ ≠ 0. Amount gap = total × (p₂ - p₁).

Worked example

Moving from 20% to 25% adds 5 percentage points. Relative to the initial 20%, that is a 25% increase. On a fixed total of 200, the amount changes from 40 to 50.

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Frequently asked questions

Can the gap be negative?

Yes. Going from 60% to 50% is a change of -10 percentage points.

What if the starting rate is zero?

The point change is still defined. Relative percentage change is undefined, so that output is omitted.

Can the groups have different totals?

The rate gap can still be compared, but multiplying it by one shared total does not recover the difference in actual counts for unequal groups.

Sources

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