Percentage Calculator

The six calculations on this page

Each block above is independent, so you can leave the others blank. Results are rounded to two decimal places. The running example below uses one pair of numbers, 250 and 287.50, so you can see how the same two values produce different answers depending on which question you ask.

1. What is X percent of Y

This is the plain share of a total: the commission on a sale, the deposit on a purchase, the VAT on a price.

2. X is what percent of Y

The inverse view: you have a part and a whole and you want the share. If the total is zero the calculator returns "Invalid input" rather than dividing by zero.

3. Percentage increase

Measures growth against the starting number, not the ending one. That choice of denominator is the whole point, and it is where most mistakes come from.

If you enter a final value lower than the original, this block returns a negative number. That is correct, not a bug: a change of −15% is a fall. An original of zero returns "Invalid input", because growth from nothing has no meaningful percentage.

4. Percentage decrease

Same starting number as the denominator, but the subtraction runs the other way so a genuine fall reads as a positive number.

5. Percentage difference

Use this when neither value is the "before" one, for example comparing two suppliers or two months side by side. It divides by the average of the two values, which makes the answer symmetric: swap the inputs and you get the same number.

6. Reverse percentage

You know the answer and the percentage, and you want the number it came from. This is the block to use for stripping VAT out of an inclusive price, covered further down.

Same two numbers, three different answers

None of these is wrong. They answer different questions. If a report quotes a percentage without saying what it divided by, the number is not yet interpretable.

Up 20 percent then down 20 percent does not return you to the start

This one costs people real money. Start at 100. Add 20% and you have 120. Now take 20% off 120: that is 24, not 20, because the 20% is charged against the larger number. You land on 96, four percent below where you started.

The shortcut is that an increase of p followed by a decrease of p always leaves you at 1 − p² of the original. A 50% gain followed by a 50% loss leaves you at 75%. An investment that halves needs to double, a 100% gain, just to break even. To undo the 20% rise from 100 to 120 you need a 16.67% cut, which is exactly what the percentage decrease block returns for 120 down to 100.

Percentage change and percentage points are not the same thing

When the number you are talking about is itself a percentage, saying it went up by a percentage is ambiguous, and news reports get this wrong constantly.

Suppose a lending rate moves from 7.00% to 7.50%. The rise is 0.5 percentage points. As a percentage change it is ((7.5 − 7) / 7) × 100 = 7.14%. Both are true statements about the same move, and they differ by a factor of fourteen. The same applies to an unemployment figure going from 32% to 34%: two percentage points, or a 6.25% relative increase.

The rule: subtract two percentages and the unit of the answer is percentage points. Divide one by the other and the unit is percent. This calculator works in percent, so if you want percentage points, simply subtract the two figures yourself.

Discounts and sale prices

For a single discount, the fastest route is to calculate what you pay rather than what you save. A jacket at R2,400 with 30% off: put 70 and 2400 into the first block and you get R1,680 directly. Putting in 30 gives you the R720 saving instead.

Stacked discounts multiply, they do not add. A 30% sale with a further 10% off at the till is not 40% off. It is 0.70 × 0.90 = 0.63, so you pay 63% of the original and the true discount is 37%. On that R2,400 jacket you pay R1,512, not the R1,440 that adding the percentages would suggest. The gap grows as the discounts get larger.

VAT at 15 percent

South African VAT has been 15% since April 2018. Adding it is the first block: 15% of R1,000 is R150, giving a VAT-inclusive price of R1,150.

Removing it is where people slip. The VAT is not 15% of the inclusive price. Taking 15% of R1,150 gives R172.50, which overstates the tax by R22.50. Use the reverse percentage block instead: R1,150 is 115% of the pre-VAT amount, so 1150 / 1.15 = R1,000, and the VAT is the R150 difference.

That 13.04% is why the decrease from 287.50 to 250 earlier came out at 13.04%: 250 plus VAT is exactly 287.50. Any VAT-inclusive price is 13.04% tax and 86.96% goods.

Tips

Ten percent is the usual baseline in South Africa, with 15% for service worth rewarding. On a restaurant bill of R680, 10% is R68 for a total of R748, and 15% is R102 for a total of R782. The mental shortcut works anywhere: move the decimal one place left for 10%, halve that for 5%, and add the two together for 15%.

Check whether a service charge has already been added before tipping, which is common for larger tables. Tipping on a total that already includes a service charge means paying a percentage on top of a percentage.

Limits worth knowing

Answers are rounded to two decimals, so a long chain of calculations copied by hand can drift by a cent or two. The increase and decrease blocks reject an original value of zero, and the reverse block rejects a percentage of zero, because those divisions are undefined. Percentage difference assumes both values sit on the same side of zero. Two exact opposites such as 5 and −5 average to zero, which makes the ratio undefined, so the block reports invalid input rather than a misleading 0%. Values that merely straddle zero still push the average close to zero and make the answer explode: 5 against −4.99 reports 199,800%. That number is arithmetically correct but rarely meaningful, so compare like with like.

Frequently asked questions

How do I work out a percentage in my head?

Find 10% by shifting the decimal point one place left, then build from it. For 35% of 240: 10% is 24, so 30% is 72, and 5% is 12, giving 84. Percentages are also reversible, so 8% of 50 equals 50% of 8, which is 4.

Why does percentage increase show a negative number?

Because the final value you entered is smaller than the original. The formula subtracts the original from the final, so a fall gives a negative result. Use the percentage decrease block if you would rather see it as a positive figure.

Is percentage difference the same as percentage change?

No. Percentage change divides by the starting value and has a direction. Percentage difference divides by the average of the two values and has no direction, so swapping the inputs gives the same answer. Use change for before and after, and difference for two things being compared.

How do I get the price before VAT?

Enter the inclusive price and 115 into the reverse percentage block. R2,300 divided by 1.15 gives R2,000, so the VAT included was R300. Do not take 15% of the inclusive price, which is a different and larger number.

Why do I get an invalid input message?

The calculator refuses divisions it cannot define. That means a total of zero when asking what percentage a value is, an original of zero for an increase or decrease, a percentage of zero in the reverse block, and two zeros in percentage difference. Change the offending field and the answer appears immediately.