Percent Difference Calculator

How percentage difference works

Quick answer: divide the gap between the two values by their average, then multiply by 100. For 20 and 30 the gap is 10, the average is 25, and 10 ÷ 25 × 100 = 40%.

What is percentage difference?

Percentage difference compares two values when neither one is the original. It uses their average as the base, so swapping the values gives the same answer. That symmetry is what separates it from percent change, which divides by the starting value and so depends on the order. In laboratory work the same measure is called relative percent difference, or RPD.

Percentage difference formula

This is the formula to calculate percentage difference, also called the percent difference formula. For positive numbers the bars around a and b in the denominator can be dropped, giving abs(a − b) ÷ ((a + b) ÷ 2). Averaging the absolute values is a convention that keeps the result defined for negative inputs, and the percentage difference calculator states the formula it used.

How to find the percentage difference between two numbers (step by step)

1. 1Subtract the smaller value from the larger to get the gap.
2. 2Add the two values and divide by 2 to get their average.
3. 3Divide the gap by the average.
4. 4Multiply by 100 and add the percent sign.

That is how to calculate percentage difference between two figures. Neither value has to be chosen as the starting point, so the order never matters.

How to calculate percent difference in your head

How to find percent difference without a calculator: find the gap, halve the sum, then divide. For 45 and 60 the gap is 15 and the sum is 105, so the average is 52.5. Fifteen is a little under 30% of 52.5, which matches the exact 28.57%. As a sanity check, a calculated percent difference can never be negative, and for two positive values it can never exceed 200%. If you get either, one of the inputs or steps is wrong.

Percentage difference between two prices

A price difference is the gap in money: $60 minus $45 is $15. To calculate a price difference as a percentage, scale that gap to the typical price: $15 ÷ $52.50 = 28.57%. If you instead want to say how much dearer the $60 item is than the $45 one, that is a change from $45, and the answer is +33.3%. Use the percentage change calculator for that wording.

Relative percent difference (RPD)

Two duplicate measurements of 12.5 and 13.1 differ by 0.6 on an average of 12.8, which is an RPD of 4.69%. Labs typically compare the figure with a tolerance set by their own method, so the calculator reports the number and leaves the pass or fail judgement to you. Enter the two readings into the calculator above and it works as an RPD calculator.

How large can percentage difference get?

For two non-negative values the percentage difference runs from 0% to 200%. It is 0% when the values match and 200% when one of them is 0. It equals exactly 100% when one value is three times the other, as with 10 and 30, because the gap then equals the average.

Percentage difference vs percentage change vs percent error

Use percentage difference when two values are peers, such as two shops, two groups or two instruments. Use the percentage change calculator when one value came first. Use the percent error calculator when one value is a known true or accepted value.

Where percentage difference is used

The percentage difference between two numbers answers "how far apart are these?" in many settings: two suppliers' quotes, sales in two regions, the conversion rates of two versions in an A/B test, or two replicate lab readings. Physics and chemistry courses set it as a standard exercise, usually as the percent difference between two numbers measured in the same experiment. The reference value is deliberately missing, which is both its strength and, as the next section shows, its limit.

When percentage difference is useful and when it misleads

It is useful for comparing two measurements, two quotes or two samples without privileging either. It misleads in four cases:

• One value is clearly the baseline. For 100 and 200 the difference is 66.7%, but the second figure is 100% higher than the first. The smaller number hides the size of the jump.
• One value is zero or close to it. A pair containing 0 gives exactly 200%, and 0.1 and 30 give 198.7%, so the percentage says almost nothing about size.
• The values are percentages. A rate of 40% against 50% is a 10 point gap; the guide on percentage points explains why you should not call it 10%.
• The same pair can be framed three ways. 20 and 30 are 40% apart, 30 is 50% more than 20, and 20 is 33.3% less than 30. All three are correct, so state which one you mean, and show the absolute gap beside any percentage.

Percentage difference examples

Six pairs worked out with the formula:

Percentage difference code

Both versions reproduce the examples above (40%, 28.57%, 22.22%, 4%, 100%, 4.69% and 66.67%), average the absolute values for the base and refuse two zeros. percentChangeFrom is included so you can show the contrast with percent change.

JavaScript

1function finite(name, v) {2  if (typeof v !== "number" || !Number.isFinite(v)) throw new TypeError(`${name} must be a finite number`);3}4​5export function percentDifference(a, b) {6  finite("a", a);7  finite("b", b);8  const mean = (Math.abs(a) + Math.abs(b)) / 2;9  if (mean === 0) throw new RangeError("a and b must not both be 0: the percentage difference is undefined");10  return (Math.abs(a - b) / mean) * 100;11}12​13export function percentChangeFrom(start, end) {14  finite("start", start);15  finite("end", end);16  if (start === 0) throw new RangeError("start must not be 0: the change from zero is undefined");17  return ((end - start) / Math.abs(start)) * 100;18}

Python

1from decimal import Decimal2import math3​4​5def _num(name, v):6    if isinstance(v, bool) or not isinstance(v, (int, float, Decimal)) or not math.isfinite(float(v)):7        raise ValueError(f"{name} must be a finite number")8    return Decimal(str(v))9​10​11def percent_difference(a, b):12    a, b = _num("a", a), _num("b", b)13    mean = (abs(a) + abs(b)) / 214    if mean == 0:15        raise ValueError("a and b must not both be 0: the percentage difference is undefined")16    return abs(a - b) / mean * 10017​18​19def percent_change_from(start, end):20    start, end = _num("start", start), _num("end", end)21    if start == 0:22        raise ValueError("start must not be 0: the change from zero is undefined")23    return (end - start) / abs(start) * 100

percentDifference(100, 200) returns about 66.67 while percentChangeFrom(100, 200) returns 100: same pair, different question. Round only for display.

Privacy and input safety

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

• Fields accept numbers only. Text, empty fields, NaN and Infinity are rejected with a message.
• Two zeros return a clear message instead of a division error, because the average is 0 and the percentage difference is undefined.
• Negative inputs are accepted. The base is the average of the absolute values, and the result states that formula so you can compare it with other tools.
• A comma followed by exactly three digits is read as a thousands separator, so 1,200 is 1200. Any other comma is a decimal point, so 12,50 is 12.50, and a number starting with 0, such as 0,500, is read as a decimal. Mixed formats such as 1.234,5 and ambiguous entries such as 1,2,3 are refused instead of guessed. Spaces, including no-break spaces, between digit groups are ignored.

Common percentage difference mistakes

Percentage difference vs change vs error vs points

Pick by asking which number, if any, is the reference.