Percentage Point Calculator

See the change between two percentages in percentage points, as a relative percent change and in basis points.

Calculator

How to Use the Percentage Point Calculator

  1. Enter the original percentage (e.g. 6.5 for 6.5%).
  2. Enter the new percentage on the same scale (e.g. 7.25).
  3. Click Calculate.
  4. Read the change in percentage points, the relative percent change and the change in basis points.
Example: An interest rate goes from 2% to 3.5%.
Change = 3.5 − 2 = +1.5 pp (+150 bp). Relative change = (1.5 ÷ 2) × 100 = +75%.

How the Change Is Calculated

Percentage point change = new % − original %. Relative change = (new % − original %) ÷ original % × 100. Basis points = percentage points × 100. For a mortgage rate that moves from 6.5% to 7.25%: +0.75 pp, +75 bp, a relative increase of 11.54%.

Percentage points are a difference between percentages; percent is a ratio. One percentage point equals 100 basis points (bp), the unit used in bond and interest-rate markets — a quarter-point Fed move is 0.25 pp = 25 bp.

SymbolMeaning
Original %The starting rate, entered as a number (6.5 for 6.5%)
New %The later or compared rate, on the same scale
ppNew % − Original %
Relative %pp ÷ |Original %| × 100 (not shown when the original is 0)
bppp × 100

Worked Examples

  1. 1A 30-year fixed mortgage rate rises from 6.5% to 7.25%.

    7.25 − 6.5 = 0.75; 0.75 ÷ 6.5 × 100

    +0.75 pp · +75 bp · relative +11.54%

    On a $400,000 loan the monthly principal-and-interest payment rises from $2,528.27 to $2,728.71 — about $200 a month. "Rates rose 0.75 points" and "rates rose 11.5%" are both true; "rates rose 0.75%" is wrong.

  2. 2The unemployment rate falls from 4.0% to 3.5%.

    3.5 − 4.0 = −0.5; −0.5 ÷ 4 × 100

    −0.5 pp · −50 bp · relative −12.5%

    With an unchanged labor force, one in eight unemployed people found work.

  3. 3A candidate moves from 45% to 52% support in a poll.

    52 − 45 = 7; 7 ÷ 45 × 100

    +7 pp · relative +15.56%

    Saying the candidate "gained 7%" understates the relative change and misnames the absolute one. The same +1 pp is a 50% increase from 2%, 25% from 4% and 10% from 10%.

Which Values Should I Enter?

  • Percentages as numbers6.5 for 6.5%, not 0.065. Both fields must use the same scale.
  • Order mattersOriginal first, new second: 6.5 → 7.25 is +11.54%, but 7.25 → 6.5 is −10.34%.
  • Original of 0%The pp change is shown; a relative change from 0 is undefined, so it is left blank.
  • Negative percentagesA −2% return improving to +1% is +3 pp. The relative figure (+150%) is rarely meaningful when the sign changes; report the pp change.
  • Percent of a quantity"What is 15% of 80" or "by what percent did a price change" is a percentage-change question, not percentage points.

Reading the Result

Report percentage points for rates — interest rates, tax rates, unemployment, market shares, poll numbers — and percent for quantities such as prices, salaries and account balances.

The relative change shows how big the move is compared with the starting level: a variable rate that goes from 2% to 3% is 50% higher, so interest costs rise by about half.

Bond yields and central-bank rates are quoted in basis points: a 0.25 pp move is "25 basis points".

Common Mistakes

  • "%" for a difference of percentagesFrom 4% to 5% is 1 percentage point, not "1%".
  • Calling a relative change a point changeFrom 10% to 15% is +5 pp or +50%, never "+5%".
  • Mixing scales6.5 in one field and 0.0725 in the other.
  • Averaging relative changesAcross different starting levels, compare the pp changes instead.
  • Tax-rate headlinesA top rate raised from 37% to 39.6% is +2.6 points, a 7% relative rise.

Sources

  1. Federal Reserve — FOMC statement, December 18, 2024 — "lower the target range for the federal funds rate by 1/4 percentage point"

Frequently Asked Questions