მთავარი მიღებული
- 01"Percent" means "per hundred," so 20% is just 0.20 — turn the percent into a decimal and multiply.
- 02Increase and decrease are the base amount plus or minus that percentage of it.
- 03A reverse percentage works backward from a final price to recover the original, which is not the same as adding the percentage back.
One idea behind all of it
Every percentage problem comes from a single fact: percent means "per hundred." So 20% literally means 20 per 100, which is the fraction 20/100, which is the decimal 0.20. Once you convert a percentage into its decimal by dividing by 100 (or moving the decimal point two places left), almost every calculation becomes a plain multiplication. 45% is 0.45, 7% is 0.07, 150% is 1.50.
That single conversion is the key that unlocks the rest. "What is 20% of 80?" becomes 0.20 x 80 = 16. "What is 7% tax on $42?" becomes 0.07 x 42 = $2.94. If you can turn a percent into a decimal and multiply, you can do the majority of everyday percentage math in your head.
The cheat sheet
Six calculations that cover nearly every real situation. Each turns the percent into a decimal first.
- 01Percent of a number: multiply. 30% of 250 = 0.30 x 250 = 75.
- 02Percentage increase: base plus the percent of the base. A $50 item up 20% = 50 + (0.20 x 50) = 50 x 1.20 = $60.
- 03Percentage decrease: base minus the percent of the base. A $50 item down 20% = 50 x 0.80 = $40.
- 04Reverse percentage (find the original): divide by the multiplier. Paid $60 after a 20% markup? 60 / 1.20 = $50 original.
- 05Percent change between two numbers: (new minus old) / old x 100. From 40 to 52 = (12 / 40) x 100 = 30% increase.
- 06What percent is A of B: A / B x 100. 18 out of 24 = 18 / 24 x 100 = 75%.
Increases and decreases without the trap
The shortcut for an increase is to multiply by one-plus-the-decimal. A 20% increase multiplies by 1.20; a 5% increase multiplies by 1.05. For a decrease, multiply by one-minus-the-decimal: a 20% decrease multiplies by 0.80; a 15% discount multiplies by 0.85. This is faster than working out the amount of change and adding or subtracting it, and it is exactly what a calculator does internally.
The classic trap is assuming increases and decreases cancel. They do not. Take $100, add 20% to reach $120, then take 20% off: 120 x 0.80 = $96, not $100. The second percentage is calculated on a larger base, so the two do not undo each other. The same asymmetry means a stock that drops 50% must then rise 100% just to break even. Whenever a percentage is applied, always ask "percentage of what?"
Reverse percentages: the one people get wrong
A reverse percentage recovers an original amount from a figure that already includes a change — and it is the calculation most people fumble. Suppose a price is $60 after a 20% markup, and you want the pre-markup price. The wrong move is to take 20% off $60 (giving $48). That is wrong because the 20% was added to the smaller original, not to the $60.
The right method: the $60 represents 120% of the original, so divide by 1.20 to get the original of $50. Check it forward: $50 plus 20% is indeed $60. The same logic recovers a pre-tax price (divide by 1 plus the tax rate) or a pre-discount price (divide by 1 minus the discount rate). Reverse percentages are everywhere in shopping and accounting, which is why getting the direction right matters.
How to run any percentage calculation
For the ones you would rather not do by hand, the calculators handle every case.
- 01
Open the percentage calculator
Go to Handytool's percentage calculator. It runs in your browser with no sign-up.
- 02
Pick the calculation type
Choose percent of a number, percentage change, or the other modes depending on what you are trying to find.
- 03
Enter your numbers
Type the values. The tool applies the right formula so you do not have to remember which one to use.
- 04
For sales, try the discount calculator
When you are working out a sale price and how much you save, the discount calculator is purpose-built for it.
Percentage FAQ
How do I calculate a percentage of a number?
Turn the percent into a decimal by dividing by 100, then multiply. 30% of 250 is 0.30 x 250 = 75. That single step handles tips, tax, and discounts.
How do I work out a reverse percentage?
Divide by the multiplier, not subtract. If $60 already includes a 20% markup, it is 120% of the original, so 60 / 1.20 = $50. Taking 20% off $60 gives the wrong answer because the percentage was applied to the smaller original amount.
What is the percentage change formula?
Percent change is (new value minus old value) divided by the old value, times 100. Going from 40 to 52 is (12 / 40) x 100 = 30% increase. A negative result means a decrease.
Why don't a percentage increase and decrease cancel out?
Because each is calculated on a different base. Adding 20% to $100 gives $120, but taking 20% off $120 gives $96, since the second 20% is of the larger amount. They only cancel if applied to the same base.