Percentage Points vs Percent: What Is a Percentage Point?

What is a percentage point?

Quick answer: a percentage point is one unit of the difference between two percentages. A rate that moves from 40% to 44% has risen by 4 percentage points. The same move is a 10% relative increase, because 4 ÷ 40 = 0.10.

The unit is written pp, pts or simply points. It applies to anything already expressed as a percentage of a whole: an unemployment rate, an interest rate, a vote share, an inflation rate. It measures distance on the 0 to 100 scale, so 4 points is the same gap at 40% as at 4%. People also write "percent points", but the standard term is percentage points.

Percent vs percentage points

The two answer different questions about the same two numbers. A percentage point change is the absolute gap, the ending rate minus the starting rate. A percent change is that gap divided by the starting rate.

The relative figure depends on the base, which is why it looks dramatic when rates are small. Two points on a 4% rate is a 50% rise. Two points on a 40% rate is 5%. The gap in points is 2 both times.

From 4% to 6% is +2 points and +50%. From 6% to 4% is −2 points but −33.33%, because the base is now 6. The points are symmetric and the percentages are not.

How to calculate a percentage point change

1. 1Write the starting and ending rates as percentages of the same whole.
2. 2Subtract the starting rate from the ending rate. The result is the change in percentage points, and its sign gives the direction.
3. 3For the relative change, divide that difference by the starting rate and multiply by 100.

The same subtraction gives a percentage point difference between two groups: 52% of one group and 47% of another are 5 points apart. To apply a known change, add the points to the rate: 4.5% less 0.25 points is 4.25%.

Percentage points examples

Percentage points vs basis points

A basis point is one hundredth of a percentage point, so 1 point is 100 basis points. 25 basis points is 0.25 points and 150 basis points is 1.5 points. To convert, divide basis points by 100 to get points, or multiply points by 100.

Percentage points code

Both versions reproduce the examples above (2 and 50, 0.25 and 5.88, 6 and 13.04, 6.25 and 5.54), return no relative change when the starting rate is 0 and reject non-numeric input.

JavaScript

1function finite(name, v) {2  if (typeof v !== "number" || !Number.isFinite(v)) throw new TypeError(`${name} must be a finite number`);3}4​5function checkDecimals(decimals) {6  if (!Number.isInteger(decimals) || decimals < 0 || decimals > 10) throw new RangeError("decimals must be a whole number from 0 to 10");7}8​9export function percentagePointChange(start, end, decimals = 2) {10  finite("start", start);11  finite("end", end);12  checkDecimals(decimals);13  const points = Number((end - start).toFixed(decimals));14  const relativePercent = start === 0 ? null : Number((((end - start) / Math.abs(start)) * 100).toFixed(decimals));15  return { points, relativePercent };16}17​18export function addPoints(rate, points, decimals = 2) {19  finite("rate", rate);20  finite("points", points);21  checkDecimals(decimals);22  return Number((rate + points).toFixed(decimals));23}24​25export function addPercent(rate, percent, decimals = 2) {26  finite("rate", rate);27  finite("percent", percent);28  checkDecimals(decimals);29  return Number((rate * (1 + percent / 100)).toFixed(decimals));30}31​32export function parseRate(raw) {33  const s = String(raw).trim().replace(/%$/, "").replace(",", ".");34  return /^[+-]?(\d+\.?\d*|\.\d+)$/.test(s) ? Number(s) : NaN;35}

Python

1from decimal import Decimal, ROUND_HALF_UP, InvalidOperation2​3​4def _rate(name, v):5    if isinstance(v, bool) or not isinstance(v, (int, float, str, Decimal)):6        raise ValueError(f"{name} must be a number")7    try:8        d = Decimal(str(v).strip().rstrip("%").replace(",", "."))9    except InvalidOperation:10        raise ValueError(f"{name} must be a number")11    if not d.is_finite():12        raise ValueError(f"{name} must be a finite number")13    return d14​15​16def _round(d, decimals):17    if not isinstance(decimals, int) or isinstance(decimals, bool) or not 0 <= decimals <= 10:18        raise ValueError("decimals must be a whole number from 0 to 10")19    return d.quantize(Decimal(1).scaleb(-decimals), rounding=ROUND_HALF_UP)20​21​22def percentage_point_change(start, end, decimals=2):23    s, e = _rate("start", start), _rate("end", end)24    points = _round(e - s, decimals)25    relative = None if s == 0 else _round((e - s) / abs(s) * 100, decimals)26    return points, relative27​28​29def add_points(rate, points, decimals=2):30    return _round(_rate("rate", rate) + _rate("points", points), decimals)31​32​33def add_percent(rate, percent, decimals=2):34    return _round(_rate("rate", rate) * (1 + _rate("percent", percent) / 100), decimals)

percentagePointChange(4, 6) returns { points: 2, relativePercent: 50 }. The relative change divides by the absolute starting rate, the same convention as the percentage change calculator. The Python version rounds half up with Decimal, the usual school convention, and returns Decimals, so 2 prints as 2.00.

Privacy and input safety

Values are calculated in your browser. The rates you enter are not sent to a server or stored.

Fields accept numbers only, with an optional trailing % sign. Text, empty fields, NaN and Infinity are rejected with a message, and nothing you type is ever evaluated as code.

A starting rate of 0 returns the points and shows the percent change as undefined instead of dividing by zero. A comma decimal (4,25) is read as 4.25, and decimal places are limited to a whole number from 0 to 10.

Common percentage point mistakes

Percentage points vs percent change vs basis points vs percent difference

The first two rows are the pair people confuse. Basis points are a change of unit, and percent difference is the version with no direction, which the percentage difference calculator handles. When you report a change in a rate, give the points and the two rates, and add the percent only if the relative size matters.