Percent change and percentage points are not the same

A rate moves from 4% to 6%. One report says it rose 2 points. Another says it rose 50 percent. Both are describing exactly the same move, and both are correct.

This confusion turns up constantly in news and business writing, and it survives because neither version is a lie. They answer different questions, and the difference between 2 and 50 is large enough to be worth a paragraph.

Two questions, two answers

When the thing that moved is itself a percentage, there are two honest ways to describe the move.

1. The difference, in percentage points: 6 − 4 = 2 percentage points. Plain subtraction.
2. The percent change, measured against the starting value: (6 − 4) ÷ 4 × 100 = 50%.

Neither is a rounding or a restatement of the other. "Up 50 percent" reads as alarming; "up 2 points" reads as mild. Same two numbers. Whoever picks the framing picks the reaction, so it is worth knowing which one you are being handed.

The rule for percent change

percent change = (new − old) ÷ old × 100

The whole method lives in the denominator. You divide by where you started, never by where you ended up. Get that backwards and every answer is wrong in a direction that looks plausible.

Percentage points need no formula at all. If both numbers are percentages, subtract them.

Up and down are not symmetric

Go from 4% to 6% and back again. In points: +2, then −2. Symmetric.

In percent change: up is (6 − 4) ÷ 4 × 100 = +50%, and back down is (4 − 6) ÷ 6 × 100 = −33.33%. A 50% rise is undone by a 33.33% fall, not by a 50% fall, because the denominator changed underneath you.

A worked example with money

A price goes from $200 to $250. The change is (250 − 200) ÷ 200 × 100 = +25%, a raw difference of $50.

Now the shop runs 25% off that new price: 250 × 0.75 = $187.50. Up 25% and then down 25% has not returned you to $200. It has left you at (187.50 − 200) ÷ 200 × 100 = −6.25% against where you began.

The discount that would actually restore the old price is (200 − 250) ÷ 250 × 100 = −20%. Check it: 250 × 0.80 = $200.00. Exact.

Percent changes do not add. They multiply: 1.25 × 0.75 = 0.9375, which is the 6.25% shortfall written another way.

Which one applies to your numbers

• If the two numbers are themselves percentages — interest rates, tax rates, market share, turnout, defect rates — then both readings exist, and you have to say which you mean.
• If the two numbers are counts or amounts — dollars, units, visitors, headcount — only percent change applies. "Percentage points" means nothing there. A shop going from 200 to 250 customers did not rise 50 points.

Interest rates, where it costs money

A rate moves from 3% to 3.5%. That is 0.5 percentage points, and (3.5 − 3) ÷ 3 × 100 = 16.67% in relative terms.

For the interest you pay, the relative figure is the one that bites: the interest charged on a given balance is roughly proportional to the rate, so it climbs by something near a sixth. The half-point sounds like nothing and is not nothing. Your actual monthly payment is a separate calculation, because it mixes interest with principal — neither figure above is the payment change.

Two places percent change stops working

• Starting from zero. (5 − 0) ÷ 0 has no value. Growth from nothing has no percentage; quote the raw difference and say so.
• A negative starting value. From −5 to 5 the formula gives (5 − (−5)) ÷ (−5) × 100 = −200%, which describes a rise as a fall. When the base is negative the answer is not wrong so much as meaningless. Use the difference.

Saying it so nobody can misread it

Write both numbers when the stakes are real: "the rate rose 2 percentage points, from 4% to 6% — a 50% increase." That sentence cannot be misquoted, and it takes six extra words.

The free Percent Change tool takes a From and a To and reports the percent change alongside the raw difference. Those two outputs are exactly the two readings above: if the numbers you typed are themselves percentages, that raw difference is your percentage-point figure. It runs on your device and keeps nothing.