Percentage Calculator

To find a percentage of a number, divide the percentage by 100 and multiply: 15% of 200 is 200 × 0.15 = 30. Add that back and 200 increased by 15% is 230; subtract it and 200 decreased by 15% is 170. Those three numbers are what the Percentage Calculator returns for a percent of 15 and a value of 200, and almost every other percentage question is a rearrangement of that same line — what percent 30 is of 200 (30 ÷ 200 × 100 = 15%), what a price was before a 20% discount (divide by 0.80, never add 20% back), and why a 20% rise followed by a 20% fall leaves you holding 96, not 100.

This guide covers each percentage operation separately: the formula, a worked example you can check digit by digit, and a table of computed figures you can read an answer straight out of. It ends with mental-math shortcuts and the places percentages actually turn up — tips, sales tax, interest, margins and grades.

How to find a percentage of a number

This is the operation people mean when they say "calculate a percentage."

Result = value × (percent ÷ 100)

Worked through on 18% of 62.50: divide 18 by 100 to get 0.18, then multiply 62.50 × 0.18 = 11.25. Adding it gives 73.75; subtracting it gives 51.25.

Percent	Value	Percent of value	Value increased	Value decreased
5%	200	10.00	210.00	190.00
8%	45	3.60	48.60	41.40
12%	250	30.00	280.00	220.00
15%	200	30.00	230.00	170.00
18%	62.50	11.25	73.75	51.25
20%	1,250	250.00	1,500.00	1,000.00
25%	80	20.00	100.00	60.00
30%	149.99	45.00	194.99	104.99
40%	75	30.00	105.00	45.00
150%	80	120.00	200.00	−40.00

Two things that trip people up sit in that table. The 30% row shows why the calculator rounds to the cent: 30% of 149.99 is 44.997 exactly, which becomes 45.00, so the increased figure is 194.99 rather than 194.987. And the last row shows a percentage above 100 behaving perfectly normally — 150% of 80 is 120, more than the whole, which is what you get whenever growth more than doubles something or a markup exceeds cost. Decreasing 80 by 150% takes you past zero to −40, which is arithmetically correct and usually a sign you meant a different question.

How to work out what percent one number is of another

Reverse the multiplication and you get the "part of a whole" formula:

Percent = (part ÷ whole) × 100

If 43 of 50 questions are correct, 43 ÷ 50 = 0.86, and 0.86 × 100 = 86%.

Part	Whole	Part ÷ whole	Percent
30	200	0.15	15.00%
43	50	0.86	86.00%
7	9	0.7778	77.78%
18	24	0.75	75.00%
250	4,000	0.0625	6.25%
1,240	980	1.2653	126.53%

The only real decision here is which number is the whole. It is the one you are measuring against — total questions, total revenue, total headcount — and it goes on the bottom. Getting that backwards is the most common percentage error there is, and it is silent: 7 ÷ 9 gives 77.78% while 9 ÷ 7 gives 128.57%, and both look like plausible answers.

The last row is a reminder that the part can exceed the whole. If you forecast 980 units and sold 1,240, you hit 126.53% of target.

How to add a percentage to a number

Adding a percentage has a long form and a shortcut, and the shortcut is the one worth learning:

New value = value + (value × percent ÷ 100) Shortcut: new value = value × (1 + percent ÷ 100)

A salary of $52,000 with a 4.5% raise: 52,000 × 1.045 = $54,340. The long way — 52,000 × 0.045 = $2,340, then 52,000 + 2,340 — gives the same answer with an extra step.

The shortcut turns every increase and decrease into a single multiplier, which is what makes chains of percentages tractable later on.

Change	Multiplier	Applied to $250
+3%	1.03	$257.50
+5%	1.05	$262.50
+8%	1.08	$270.00
+10%	1.10	$275.00
+15%	1.15	$287.50
+20%	1.20	$300.00
+50%	1.50	$375.00
−5%	0.95	$237.50
−10%	0.90	$225.00
−15%	0.85	$212.50
−20%	0.80	$200.00
−25%	0.75	$187.50
−40%	0.60	$150.00

Adding a percentage is what sales tax, tips, markups and raises all are. If you sell, it is also how a markup is applied to cost — and markup is not the same thing as margin, which the Profit Margin Calculator separates properly.

How to subtract a percentage: discounts and markdowns

New value = value × (1 − percent ÷ 100)

A $499 jacket at 30% off: 499 × 0.70 = $349.30, a saving of $149.70. Note that you can go straight to the price you pay without calculating the discount first — 70% of 499 is the sale price.

Original price	10% off	20% off	25% off	30% off	40% off	50% off	70% off
$20.00	$18.00	$16.00	$15.00	$14.00	$12.00	$10.00	$6.00
$35.00	$31.50	$28.00	$26.25	$24.50	$21.00	$17.50	$10.50
$50.00	$45.00	$40.00	$37.50	$35.00	$30.00	$25.00	$15.00
$80.00	$72.00	$64.00	$60.00	$56.00	$48.00	$40.00	$24.00
$120.00	$108.00	$96.00	$90.00	$84.00	$72.00	$60.00	$36.00
$250.00	$225.00	$200.00	$187.50	$175.00	$150.00	$125.00	$75.00
$499.00	$449.10	$399.20	$374.25	$349.30	$299.40	$249.50	$149.70

Stacked discounts do not add. "20% off, then an extra 10% off at checkout" is 0.80 × 0.90 = 0.72, so 28% off, not 30%. On the $120 row that is $86.40 rather than the $84.00 a flat 30% would give — a $2.40 gap that gets wider on bigger baskets. Retailers know this; the second discount is always applied to the already-reduced price. If you are the one setting the markdown, the Discount and Margin Calculator shows what each price cut does to the margin underneath it.

How to calculate percentage change between two numbers

When you have a before and an after and want the movement between them:

Change % = ((new − old) ÷ old) × 100

Revenue moving from $45,000 to $52,000: the difference is $7,000, and 7,000 ÷ 45,000 = 0.15556, so +15.56%. A negative result is a decrease; the formula handles both directions with no change.

Old value	New value	Difference	Percentage change
200	230	+30	+15.00%
80	100	+20	+25.00%
100	80	−20	−20.00%
50	75	+25	+50.00%
75	50	−25	−33.33%
1,200	1,500	+300	+25.00%
45,000	52,000	+7,000	+15.56%
3.20	4.15	+0.95	+29.69%
250	250	0	0.00%
40	120	+80	+200.00%

Rows two and three are the point of the whole table. Going 80 → 100 is a 25% increase; going 100 → 80 is a 20% decrease. Same $20 moved, different percentage, because the denominator changed. Percentage change is always measured against where you started, so the two directions are never mirror images.

The old value goes on the bottom. Dividing by the new value instead is the single most frequent mistake in this formula and it always understates a rise and overstates a fall.

How to reverse a percentage and find the original number

If you know the amount after a change and want the amount before it, you divide by the multiplier rather than reversing the addition:

Original before an increase = final ÷ (1 + percent ÷ 100) Original before a discount = final ÷ (1 − percent ÷ 100)

You paid $84.00 after 20% off. The original was 84 ÷ 0.80 = $105.00. Adding 20% back to $84 gives $100.80 — wrong, because that 20% is being taken on the smaller number.

Amount you have	What happened to it	The division	Original amount
$84.00	20% discount applied	84.00 ÷ 0.80	$105.00
$60.00	25% discount applied	60.00 ÷ 0.75	$80.00
$46.75	15% discount applied	46.75 ÷ 0.85	$55.00
$107.99	8% sales tax added	107.99 ÷ 1.08	$99.99
$230.00	15% increase applied	230.00 ÷ 1.15	$200.00
$1,500.00	20% increase applied	1,500.00 ÷ 1.20	$1,250.00
$2,400.00	60% markup applied	2,400.00 ÷ 1.60	$1,500.00

This is the operation behind stripping tax out of a gross figure — a receipt total of $107.99 including 8% tax breaks into $99.99 of goods and $8.00 of tax, and the Sales Tax Calculator does it in both directions for 2026 US rates. Outside the US the same division backs VAT out of a gross price, which is what the VAT Calculator is for.

It is also how you set a price that survives a discount. If you need $55 after a 15% promotion, list at 55 ÷ 0.85 = $64.71, not $63.25.

Percentage points versus percent

These are different units and mixing them produces answers that are off by large factors.

A percentage point is the arithmetic gap between two percentages. A percent change is that gap measured relative to where it started.

From	To	Change in percentage points	Relative percent change
4%	6%	+2 pp	+50.00%
2%	3%	+1 pp	+50.00%
1%	2%	+1 pp	+100.00%
50%	55%	+5 pp	+10.00%
20%	15%	−5 pp	−25.00%
6.5%	7.0%	+0.5 pp	+7.69%
3.2%	2.8%	−0.4 pp	−12.50%

A default rate moving from 4% to 6% is up two percentage points and up 50 percent. Both statements are true and they describe the same event; a headline that picks whichever sounds more dramatic is not lying, just choosing.

The money version makes it concrete. A management fee rising from 2% to 3% on a $50,000 balance is one percentage point — and $1,000 a year becoming $1,500, which is 50% more money out the door. On a mortgage the same logic applies to rate quotes: a move from 6.5% to 7.0% is half a percentage point but 7.69% more interest per dollar borrowed, and the Mortgage Calculator shows what that does to a monthly payment.

Rule of thumb: if both numbers are already percentages, say "percentage points" for the subtraction and "percent" only when you have divided.

How to calculate percentage error

Percentage error compares an estimate, measurement or forecast against the true value:

Percentage error = ((measured − actual) ÷ actual) × 100

A scale reads 48 kg for something that actually weighs 50 kg: (48 − 50) ÷ 50 = −0.04, so −4.00%. The sign tells you the direction — negative is an underestimate, positive an overestimate. Drop the sign and you have absolute percentage error, which is what forecasting accuracy is usually reported as.

Measured or forecast	Actual value	Difference	Percentage error
102	100	+2	+2.00%
9.7	10	−0.3	−3.00%
48	50	−2	−4.00%
3.95	4.00	−0.05	−1.25%
1,150	1,000	+150	+15.00%
27,500	30,000	−2,500	−8.33%

The actual value is the denominator, always. Dividing by the measurement instead gives a different number that means nothing in particular — forecasting 27,500 against an actual 30,000 is an 8.33% error, not the 9.09% you would get from the wrong denominator.

Why a 20% gain and a 20% loss leave you at 96

Percentages compound. They apply to whatever the number is at that moment, not to where it started, so equal-looking moves in opposite directions do not cancel.

Take $10,000. Up 20% is $12,000. Down 20% from $12,000 is $9,600 — because that second 20% is $2,400, not the $2,000 you gained. Net position: −4%. Reverse the order and you get the same answer: down 20% is $8,000, up 20% is $9,600. In multiplier terms, 1.20 × 0.80 = 0.96, and multiplication does not care about order.

Start	First change	Second change	End value	Net change
100	+10%	−10%	99.00	−1.00%
100	+20%	−20%	96.00	−4.00%
100	−20%	+20%	96.00	−4.00%
100	−30%	+30%	91.00	−9.00%
100	+50%	−50%	75.00	−25.00%
100	+100%	−50%	100.00	0.00%
100	+10%	+10%	121.00	+21.00%

The consequence for anything that can lose value is that recovery is always harder than the loss:

Loss taken	Value left from 100	Gain needed to get back to 100
−10%	90.00	+11.11%
−20%	80.00	+25.00%
−25%	75.00	+33.33%
−40%	60.00	+66.67%
−50%	50.00	+100.00%
−60%	40.00	+150.00%
−75%	25.00	+300.00%
−90%	10.00	+900.00%

Compounding works the same way upward, which is the whole argument for long holding periods. Growth of 7% a year for ten years is not 70% — it is 1.07 raised to the tenth power, or 1.9672, a gain of 96.72%. A $10,000 balance becomes $19,671.51. The Compound Interest Calculator runs that out year by year, and the Investment ROI Calculator converts a total return into the annual rate that produced it.

Percent, decimal and fraction conversions

Three rules cover every conversion. To go from percent to decimal, divide by 100. To go from decimal to percent, multiply by 100. To go from a fraction to a percent, do the division first and then multiply by 100.

Fraction	Decimal	Percent
1/100	0.01	1%
1/50	0.02	2%
1/20	0.05	5%
1/10	0.10	10%
1/8	0.125	12.5%
1/6	0.1667	16.67%
1/5	0.20	20%
1/4	0.25	25%
1/3	0.3333	33.33%
3/8	0.375	37.5%
2/5	0.40	40%
1/2	0.50	50%
3/5	0.60	60%
5/8	0.625	62.5%
2/3	0.6667	66.67%
3/4	0.75	75%
4/5	0.80	80%
7/8	0.875	87.5%
1	1.00	100%
5/4	1.25	125%
3/2	1.50	150%
2	2.00	200%

Knowing the eighths is worth more than it looks, because retail prices cluster around them — 12.5%, 37.5%, 62.5% and 87.5% all come out of a denominator of 8, and spotting that 37.5% off is "three eighths off" turns a calculator problem into a division by 8.

Mental math tricks for percentages

• 10% is a decimal shift. 10% of 68 is 6.8. Move the point one place left and stop.
• 1% is two places. 1% of 68 is 0.68. Everything else can be built from 10% and 1%.
• 5% is half of 10%. 10% of 68 is 6.8, so 5% is 3.4.
• 20% is double 10%. 6.8 doubled is 13.6.
• 15% is 10% plus 5%. 6.8 + 3.4 = 10.2.
• 25% is a quarter — divide by 4. 25% of 68 is 17. Likewise 50% is half and 12.5% is an eighth.
• Build odd percentages from pieces. 35% of 80 = 25% (20) + 10% (8) = 28. An 18% tip is 20% minus 2%: on $86.40 that is 17.28 − 1.73 = $15.55.
• Percentages are reversible: X% of Y equals Y% of X. This is the best trick on the list and almost nobody knows it. 8% of 25 is awkward; 25% of 8 is obviously 2 — and they are the same number, because both are 0.08 × 25. Similarly 4% of 75 is 75% of 4 = 3, and 16% of 50 is 50% of 16 = 8. Whenever one side is a friendly number, flip it.

The reversal works because multiplication commutes: X% of Y is (X ÷ 100) × Y, and Y% of X is (Y ÷ 100) × X. Same two numbers, same product.

Where percentages show up day to day

Tips. A tip is a straight percentage of the bill, and 2026 US table-service norms run roughly 15% to 20%, with 25% for exceptional service.

Bill	15% tip	18% tip	20% tip	25% tip
$18.00	$2.70	$3.24	$3.60	$4.50
$32.50	$4.88	$5.85	$6.50	$8.13
$50.00	$7.50	$9.00	$10.00	$12.50
$86.40	$12.96	$15.55	$17.28	$21.60
$124.75	$18.71	$22.46	$24.95	$31.19

Sales tax. There is no national US sales tax in 2026; rates are set by state and locality and combined rates typically land somewhere between 0% and about 10%. Tax is a percentage increase on the pre-tax price, so $99.99 at 8% becomes $107.99.

Interest. Simple interest is one percentage of the principal per period: 5% on $1,000 is $50 a year. Compound interest applies the percentage to the growing balance — $1,000 at 5% for ten years is 1,000 × 1.05^10 = $1,628.89, not the $1,500 simple interest would give. On the borrowing side the same compounding is what makes minimum payments so expensive; the Credit Card Payoff Calculator shows the arithmetic from the other direction.

Margins. Margin and markup are both percentages and they are not interchangeable. Cost $60, sell at $100: margin is profit over price, 40 ÷ 100 = 40%; markup is profit over cost, 40 ÷ 60 = 66.67%. Pricing off the wrong one is how sellers end up short, which how to price products for profit walks through in detail.

Grades and targets. A score is a part-of-whole percentage: 43 of 50 is 86%. Weighted grades are a percentage of a percentage — homework worth 30% of the grade at 92% contributes 27.6 points, and coursework worth 70% at 81% contributes 56.7, for a final 84.3%.

Budgets and pay. Percentage splits are how most budgeting frameworks work; the 50/30/20 budget rule is three percentages of take-home pay, and the Take-Home Pay Calculator gets you the figure those percentages apply to.

Common mistakes

Adding the percentage back to reverse a discount. After 20% off you paid $84. Adding 20% to $84 gives $100.80; the real original was $105.00, because the discount was taken from the larger number. Always divide by the multiplier.

Confusing percentage points with percent. A rate moving from 4% to 6% is two percentage points and a 50% increase. Reporting the 2 as "2%" understates the change by a factor of 25.

Assuming equal up and down moves cancel. Up 20% then down 20% is 1.20 × 0.80 = 0.96, so you end 4% behind. The bigger the swings, the worse it gets — up 50% then down 50% leaves you 25% down.

Using the wrong base in percentage change. The old value belongs in the denominator. Going 80 → 100 is +25%, not the +20% you get by dividing by 100 instead of 80.

Adding stacked discounts together. 20% off followed by an extra 10% off is 28% off, not 30%. On a $120 basket that is $86.40 rather than $84.00.

Mixing up margin and markup. A $60 cost sold at $100 is a 40% margin and a 66.67% markup. Setting a "40% markup" when you meant margin prices the item at $84 and quietly removes a third of the profit you planned.

Related calculators

• Percentage Calculator — percent of a value, plus that value increased and decreased
• Discount and Margin Calculator — what a markdown does to the margin underneath it
• Sales Tax Calculator — add tax to a price or strip it back out of a gross total
• Profit Margin Calculator — margin and markup from the same cost and price
• Compound Interest Calculator — a percentage applied over and over, year by year
• Investment ROI Calculator — turn a total return into an annual percentage
• Salary to Hourly Calculator — convert a salary, then apply a raise percentage to it