Percentage Increase vs Percentage Points

Two true sentences can describe one change in a rate, and they sound like they disagree. A savings account moves from 2% interest to 3% interest. The difference is 1 percentage point. Relative to the old rate, the increase is 1/2 = 50%. Neither speaker is doing fantasy math. They are answering different questions, and English uses the word “percent” for both.

If you remember a single habit, make it this: when both numbers already wear a percent sign, say whether you subtracted or divided.

Percentage points are a subtraction

Percentage points (sometimes written pp, or p.p.) measure the gap between two percentages by ordinary subtraction.

• 10% to 12% is 2 percentage points
• 40% support to 50% support is 10 percentage points
• 19% VAT to 23% VAT is 4 percentage points
• 3.00% to 3.25% is 0.25 percentage points, which bond traders also call 25 basis points

There is no division. The “point” is already in percent units. This is the right tool when the rate itself is the object: a contract clause, a tax band, a poll share, a pass mark.

Relative change divides by the starting rate

Apply the ordinary percent-change formula to the two rates, treating them as plain numbers:

Relative change = (new − old) / |old| × 100%

The same 1 percentage point gap is a doubling when you start at 1% and a shrug when you start at 90%. Relative change is the right tool when the starting rate is the base that matters — “our click-through doubled” — and a misleading tool when the level of the rate is what people live with. A tax that moves from 1% to 2% really does double, and it also really is only one extra cent on a euro. Report the cents as well as the percent if you are talking to someone who pays the tax.

Polls, where the mix-up is the headline

A candidate moves from 40% to 50% of decided voters.

• The share of the electorate changed by 10 percentage points.
• The candidate’s support is 25% higher than it was, relative to the old share.

“Up 10%” fits neither sentence cleanly. Readers who hear “10%” often picture a move from 40 to 44 (that is, 10% of 40, added on) or a move that is “10 percent more popular” in a vague sense. The 40-to-50 story is the 10-point story. If a journalist means the relative one, “up 25%” or “up a quarter” is available and unambiguous.

Small shares make the relative number loud. From 4% to 6% is 2 points and a 50% relative increase. A minor party can truthfully claim both “we gained 2 points” and “support rose by half.” The first tells you they are still small. The second tells you the direction was strong. Printing only the second is how a 6% party is dressed as a surge without the denominator.

Grades and cut scores

A passing bar moves from 70% to 75%. That is 5 percentage points, not “5% harder” in the relative sense (the relative change of the bar is 5/70 ≈ 7.1%). A student who scored 74% passed yesterday and fails today. Their score did not fall. The threshold moved by 5 points.

Now take the student’s own score, from 70% to 77% of the marks. That is 7 percentage points of the exam, and a 10% relative improvement on their previous percentage score (7/70 = 0.10). Teachers usually mean points when they say “you went up 7 percent” in a hallway, and they usually mean the relative figure when they talk about improvement “by 10%.” Ask which denominator they used: the exam’s total marks, or last term’s percentage.

Weighted grades add a further base problem that is not about points at all. Averaging an 80% homework (worth 10% of the course) with a 60% final (worth 50%) by taking the mean of 80 and 60 is the unweighted mistake in common percentage mistakes. Points versus relative change is a second layer. You can get either layer wrong independently.

Interest rates and central banks

Suppose a loan’s nominal rate moves from 6% to 7%.

• The rate is 1 percentage point higher.
• The rate is about 16.7% higher than it was (1/6 ≈ 0.1667).
• The monthly payment does not rise by 16.7%, and it does not rise by 1% of the payment either, except by coincidence.

On an amortizing loan the payment contains principal and interest. Interest is the part tied to the rate; principal repayment is tied to the remaining balance and the term. A 1 point move changes the interest slice a lot and the principal schedule a little, so the payment rise sits somewhere below the relative change in the rate. The way to see the actual euro change is to run both rates through the loan calculator, not to multiply the old payment by 1.167.

Central banks speak in basis points because “0.25 percentage points” is a mouthful and “a quarter of a percent” is ambiguous (a quarter of a percent of what?). 25 basis points = 0.25 percentage points = 0.25% absolute on the rate. It is not a 25% relative move unless the starting rate was 1%.

VAT and prices, a related but different pair

A standard VAT rate moving from 20% to 23% is 3 percentage points, and a 15% relative increase in the rate (3/20). The price the customer pays does not rise by 15%. If a net price is €100, the gross moves from €120 to €123, which is €3, or 2.5% more at the till (3/120). Three different percents, all defensible, describe one tax change:

1. +3 percentage points on the VAT rate
2. +15% relative change in the VAT rate
3. +2.5% change in the gross price

If you are the person paying, (3) is the price change. If you are comparing statutes, (1) is the statute change. (2) is mostly useful as a warning that relative language makes a 3-point tax move sound like a 15% price move. It is not. How to calculate VAT shows the gross formula; this section is only about naming the change.

How to write the sentence so it survives

• Prefer “from 8% to 10%, up 2 percentage points” when you mean subtraction.
• Prefer “10 is 25% higher than 8” when you mean division. Include the original number.
• Avoid “up 2%” and “up 10%” for moves between percentages. Both are commonly read the wrong way.
• If a decision or a headline depends on the figure, give the two raw percentages as well. “Support went from 40% to 50%” needs no jargon and cannot be mis-divided by a hurried reader.

The percentage change calculator computes the relative column. It will happily tell you that 8 to 10 is 25%. It cannot tell you that you wanted points. That choice is the content of the sentence, which is why a calculator page alone never quite teaches this distinction.

When the difference is too small to matter — and when it is not

On a move from 2% to 2.1%, the gap is 0.1 points and a 5% relative bump. For a household budget the cash effect may be noise. On a move from 2% to 4% in a mortgage offer, calling it “up 2%” instead of “up 2 points” can hide a payment change that is the size of a utility bill. Run the money. Name the points. If you still want the relative figure, label it as relative to the old rate, not as the change in the price.

Use both numbers when you are writing for anyone who might act. One number is a slogan. Two numbers are a measurement.