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Percentage Calculator

Five percentage questions in one place, including percent change, percent difference and percent error, which are three different numbers that people routinely mix up.

Question

Percent change is signed and asymmetric: 80 to 100 is a rise of 25 percent, but 100 back to 80 is a fall of 20 percent, because the base changes. Percent difference is symmetric because it divides by the average of the two. Percent error divides by the true value and keeps the sign, so a negative result means the measurement reads low.

Bar chart showing 80 and 100 producing a 25 percent rise one way, a 20 percent fall the other way, and a symmetric 22.22 percent difference, with a note on why a 50 percent loss needs a 100 percent gain. — Change divides by the start, so direction matters. Difference divides by the average, so it does not.

How to use this tool

Pick the question from the dropdown, fill in the two numbers, and the answer updates as you type. The labels change with the question, so P and Y become A and B or measured and true as appropriate, and the explanation line under the result always states the formula that was used.

The dropdown matters more than it looks, because the five questions give five different numbers from the same inputs. 80 and 100 produce 25 percent as a change one way, 20 percent the other way, and 22.2 percent as a difference. None of those is wrong. They answer different questions.

Change, difference and error are three different things

Percent change compares a new value to an old one, and divides by the old one. It is signed and it is asymmetric: going from 80 to 100 is a rise of 25 percent, coming back from 100 to 80 is a fall of only 20 percent, because the base you divide by has changed. This asymmetry is real, not a rounding quirk, and it is why a 50 percent loss needs a 100 percent gain to recover.

Percent difference is for comparing two values where neither is the reference. It divides the gap by the average of the two, which makes it symmetric: 80 against 100 gives 22.2 percent whichever one you put first. Use it when comparing two measurements of the same thing, two quotes, two lab results.

Percent error is for comparing a measurement to a known true value, and divides by the true value. It keeps its sign in this tool, so a negative result means the measurement reads low. A gravity reading of 9.80 against a true 9.81 is an error of minus 0.10 percent.

A worked check you can repeat on paper

A materials invoice rises from 46200 to 51900. The change is 51900 minus 46200, which is 5700, divided by the original 46200, giving 12.34 percent. Put A as 46200 and B as 51900 into the change mode and the tool returns the same figure.

Now reverse it as a sanity check. From 51900 back down to 46200 is minus 5700 over 51900, a fall of 10.98 percent. Not 12.34. If both directions ever gave you the same number, something would be wrong.

Mistakes that catch people out

Using percent change when there is no direction. Comparing two supplier quotes has no before and after, so percent difference is the honest number. Fix: if you cannot say which value is the base, use difference.

Adding percentages of different bases. A 10 percent rise followed by a 10 percent fall does not return to the start, it lands 1 percent low, because the second percentage acts on a bigger base. Fix: multiply the factors, 1.10 times 0.90 is 0.99.

Confusing percentage points with percent. Moving from 4 percent to 5 percent is a rise of one percentage point but a rise of 25 percent. Fix: say which one you mean, because the gap between them is enormous.

Dividing by the measured value in percent error. The definition divides by the true value. Fix: true goes on the bottom, always.

How this was checked

The formulas were verified against hand calculated values before this page went live: 15 percent of 200 returning exactly 30, 45 against 60 returning exactly 75 percent, the 80 to 100 change returning exactly 25 and its reverse exactly minus 20, and the 9.80 against 9.81 error returning minus 0.1019 percent. The asymmetry of change and the symmetry of difference were both confirmed rather than assumed.

Popular percentage questions

The percentage questions people look up most. Each opens the calculator on that answer and has its own address you can bookmark or share.

What is P percent of Y

5% of 50 5% of 100 5% of 200 5% of 500 5% of 1000 10% of 50 10% of 100 10% of 200 10% of 500 10% of 1000 12% of 50 12% of 100 12% of 200 12% of 500 12% of 1000 15% of 50 15% of 100 15% of 200 15% of 500 15% of 1000 18% of 50 18% of 100 18% of 200 18% of 500 18% of 1000 20% of 50 20% of 100 20% of 200 20% of 500 20% of 1000 25% of 50 25% of 100 25% of 200 25% of 500 25% of 1000 30% of 50 30% of 100 30% of 200 30% of 500 30% of 1000 33% of 50 33% of 100 33% of 200 33% of 500 33% of 1000 35% of 50 35% of 100 35% of 200 35% of 500 35% of 1000 40% of 50 40% of 100 40% of 200 40% of 500 40% of 1000 50% of 50 50% of 100 50% of 200 50% of 500 50% of 1000 60% of 50 60% of 100 60% of 200 60% of 500 60% of 1000 65% of 50 65% of 100 65% of 200 65% of 500 65% of 1000 70% of 50 70% of 100 70% of 200 70% of 500 70% of 1000 75% of 50 75% of 100 75% of 200 75% of 500 75% of 1000 80% of 50 80% of 100 80% of 200 80% of 500 80% of 1000 90% of 50 90% of 100 90% of 200 90% of 500 90% of 1000

X is what percent of Y

10 is what percent of 50 15 is what percent of 60 20 is what percent of 80 25 is what percent of 200 30 is what percent of 150 40 is what percent of 200 45 is what percent of 60 50 is what percent of 200 60 is what percent of 80 75 is what percent of 300 80 is what percent of 400 90 is what percent of 120 12 is what percent of 80 35 is what percent of 140 3 is what percent of 60 7 is what percent of 140

Percent change

percent change from 100 to 150 percent change from 200 to 250 percent change from 50 to 75 percent change from 80 to 100 percent change from 1000 to 1200 percent change from 60 to 45 percent change from 100 to 80 percent change from 500 to 400 percent change from 20 to 25 percent change from 150 to 100 percent change from 250 to 300 percent change from 40 to 60

Related Calculators and Reference

See also the Percent Off Calculator for discounts specifically, including stacked markdowns and what buy one get one is really worth. Grades turn into a grade point average with the GPA Calculator. Also see the Test Score Calculator: a test score as a percent and letter grade, with the most questions you can miss for a target.

See also the Tip Calculator for the everyday version, with the split and the before or after tax choice built in.

For slopes expressed as percentages, the Grade to Degrees Converter connects percent grade to angle and ratio. Probability style percentages appear in the P10, P50 and P90 percentiles reference. For percentage splits of a quantity, the Ratio and Proportion Calculator divides a total in any ratio, and the Weighted Average Calculator handles the case where each value counts differently.