A bank raises its rate from 4% to 5%. Did it go up by 1% or by 25%?
Both, depending on how you say it:
- It went up by 1 percentage point (5 − 4).
- It went up by 25 percent ((5 − 4) ÷ 4).
Mixing these up makes small changes sound huge, or huge changes sound small. That's why headlines and sales pitches love the confusion.
The two calculations
Percentage points: plain subtraction
change in points = new % − old %
Percent change: relative to where you started
percent change = (new − old) ÷ old × 100
Try any pair of numbers in the Percentage Calculator.
Examples
| Before | After | Percentage points | Percent change |
|---|---|---|---|
| 4% interest | 5% | +1 point | +25% |
| 10% conversion | 15% | +5 points | +50% |
| 2% churn | 3% | +1 point | +50% |
| 40% vote share | 36% | −4 points | −10% |
| 0.1% risk | 0.2% | +0.1 point | +100% ("risk doubles!") |
The last row is the classic scary headline. "Doubles your risk" is technically true. It's also still a 1-in-500 chance.
Why it matters
Loans. On a 1,000,000 loan, a rise from 10% to 12% is "only 2 points", but it raises the interest by 20%. See how that changes a monthly payment in How to Calculate EMI.
Product metrics. "Conversion is up 2%" could mean 5.0% → 5.1% (2 percent) or 5% → 7% (2 points, which is 40% more customers). Always say which one you mean. More on startup metrics in How to Calculate Churn Rate.
Tax and VAT. A VAT rate going from 13% to 15% is a 2-point rise, but the price only goes up by about 1.8% (115 ÷ 113).
Basis points
For small rate changes, finance uses basis points (bps):
1 basis point = 0.01 percentage points 100 bps = 1 percentage point
"The central bank raised rates by 25 bps" means 0.25 points, for example 6.00% → 6.25%.
Other percentage traps
Ups and downs don't cancel
A price drops 50%, then rises 50%. Back to where it started? No.
100 → 50 (−50%) → 75 (+50%)
After a 50% loss you need a 100% gain to get back. After a 20% loss, you need 25%.
Discounts don't add up
"30% off, plus an extra 20% off" is not 50% off.
100 × 0.70 × 0.80 = 56 → 44% off
"X% more" vs "X% of"
- "Sales were 150% of last year" → 1.5× last year.
- "Sales were 150% more than last year" → 2.5× last year.
Percent of what?
"Our users grew 300%" from 3 to 12 users is true, and it isn't impressive. When the base is small, ask for the absolute numbers.
A sentence template that avoids confusion
The rate rose from 4% to 5%, an increase of 1 percentage point (25%).
Give both numbers, plus the starting and ending values. Nobody can misread that.