PERCENTAGES

Percent Change vs Percentage Points

"Rates rose 1 point" and "rates rose 25%" can describe the same event. Here is what percent change, percentage points and percent difference each measure, and when to use which.

• 5 min read
01

Three Terms, Three Questions

Each term answers a different question:

  • Percent change: how much did a value grow or shrink compared with where it started?
  • Percentage points: how far apart are two numbers that are already percents?
  • Percent difference: how different are two values when neither one is the starting point?

Mixing them up can make a small change sound huge, or a huge one sound small.

02

Percent Change

Formula: (New − Old) ÷ Old × 100. Use it whenever there is a clear "before" and "after".

Rent $1,200 → $1,290:90 ÷ 1200 × 100=+7.5%

Direction matters. From 80 to 100 is a 25% increase, but from 100 back to 80 is a 20% decrease, because each is measured against a different starting value.

The Percentage Change Calculator does this for you and also shows the percent that would undo the change.

03

Percentage Points

Formula: New % − Old %. Use it when the two values are themselves percents, such as interest rates, tax rates, test scores or poll results.

If a savings rate goes from 4% to 5%:

  • It rose by 1 percentage point (5 − 4).
  • It rose by 25% ((5 − 4) ÷ 4 × 100).

Both statements are true. "Percentage points" describes the gap on the scale; "percent" describes the change relative to where the rate began. Saying "rates rose 1%" here is ambiguous and usually wrong.

04

Percent Difference

Formula: |A − B| ÷ ((A + B) ÷ 2) × 100. Use it to compare two values side by side when neither is the "before", for example two shops' prices or two lab measurements.

$40 vs $60:20 ÷ 50 × 100=40%

It divides by the average of the two values, so the answer is the same whichever value you list first. Compare that with percent change, which gives +50% from 40 to 60 but −33.33% from 60 to 40.

05

Which One to Use

Situation Use
A price, salary or count changed over timePercent change
A rate or score that is already a percent movedPercentage points (and percent change if useful)
Two values compared side by side, no "before"Percent difference
06

Three Common Traps

  1. Small bases make big percents. A risk rising from 1% to 2% is "up 100%" but only 1 percentage point. Headlines often quote the bigger-sounding number.
  2. Back-to-back changes don't add. Two 10% increases are 1.1 × 1.1 = 1.21, a 21% total increase, not 20%.
  3. Equal ups and downs don't cancel. Up 20% then down 20% leaves you at 96% of where you started (1.2 × 0.8 = 0.96).
07

Practice Problems

Try each one, then open the answer.

  1. Unemployment falls from 6% to 4.5%. What is the change in percentage points, and the percent change?
    Show answer−1.5 percentage points; (4.5 − 6) ÷ 6 × 100 = −25%
  2. A price goes from $80 to $100, then back to $80. What is each percent change?
    Show answer+25% (20 ÷ 80), then −20% (20 ÷ 100)
  3. What is the percent difference between 90 and 110?
    Show answer20 ÷ 100 × 100 = 20%
  4. A value increases by 50% twice. What is the total percent change?
    Show answer1.5 × 1.5 = 2.25, a 125% increase
  5. A candidate's poll number rises from 42% to 45%. Describe the change two ways.
    Show answer+3 percentage points, or 3 ÷ 42 × 100 ≈ +7.14%