CalculationTime

The percentage hub

Percentage Calculator

Percent of a number, what percent, percentage change, discounts, differences, working back to the original price - pick the question you are asking and get the answer in plain words, with the working and a picture.

Calculator

Answer any percentage question

Pick the question you are asking. Every mode explains its answer in words, shows the steps and draws a picture.

Percentage
Of this number
What is X% of a number?
answer7.2

15% of 48 is 7.2.

Show the working
  1. 15% = 15 ÷ 100 = 0.15
  2. 0.15 × 48 = 7.2
15% of the whole

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Percentage cheat sheet and worksheet

Your question worked out with its picture, every percentage formula in one table, mental-maths shortcuts, and eight practice problems with an answer key. One page.

CalculationTime cheat sheet

Percentages at a glance

Name: ______________________Date: ______________________

Your question

7.2

15% of 48 is 7.2.

  1. 15% = 15 ÷ 100 = 0.15
  2. 0.15 × 48 = 7.2

Mental shortcuts

  • 10% = move the decimal one place left; 1% = two places
  • 5% = half of 10%; 15% = 10% + 5%
  • 25% = a quarter; 50% = half; 75% = three quarters
  • x% of y = y% of x (8% of 50 = 50% of 8 = 4)
15% of the whole

Formulas

QuestionFormulaExample
p% of a numberp ÷ 100 × y20% of 150 = 30
x is what % of yx ÷ y × 10030 of 150 = 20%
x is p% of whatx ÷ (p ÷ 100)30 is 20% of 150
% change, a to b(b − a) ÷ a × 100150 to 180 = +20%
Increase / decrease y by p%y × (1 ± p ÷ 100)80 − 25% = 60
% difference|a − b| ÷ average × 10050 vs 150 = 100%
Original before p% changefinal ÷ (1 ± p ÷ 100)80 after −20% = 100
Percentage pointsp2 − p14% to 5% = +1 point

Practice

  1. 15% of 80 _______
  2. 45 is what % of 60 _______
  3. 24 is 30% of what _______
  4. 250 to 300: % change _______
  5. $60 with 35% off _______
  6. Price now $150 after a 25% rise; original? _______
  7. % difference between 8 and 12 _______
  8. Rate 3.5% to 4.25%: points and relative change _______

Answers: 1. 12 2. 75% 3. 80 4. +20% 5. $39 6. $120 7. 40% 8. up 0.75 percentage points, which is a 21.4286% increase in relative terms.

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The percentage suite

Need a specialist tool? Start here

This page handles all the everyday questions. When your job is narrower - a sale price, a tax rate, a profit margin - these focused calculators add the extra inputs and vocabulary.

In depth

Which percentage question am I asking?

Most confusion comes from picking the wrong question. Match the wording to the mode:

Wording to calculation
If the problem says…UseExample
“What is 15% of 48?”X% of a number7.2
“42 out of 60 is what percent?”X is what % of Y70%
“45 is 15% of what?”X is Y% of what300
“It went from 150 to 180”Percentage change+20%
“$200 plus 10% tax” / “$80 with 25% off”Increase or decrease220 / 60
“How different are these two prices?”Percentage difference20%
“$66 including 10% tax; what was the price?”Work back to the original60
“The rate rose from 4% to 5%”Percentage points+1 point
Fractions and their percentages
FractionPercentageDecimal
1/250%0.5
1/425%0.25
1/520%0.2
1/812.5%0.125
3/475%0.75
1/333.3333%0.3333
2/366.6667%0.6667
1/1010%0.1

Classic traps

Five percentage mistakes, with the numbers

Up 50%, down 50%

100 → 15075. The second 50% is taken of a bigger number, so you end 25% below where you began. Down 20% then up 20% gives 96, not 100.

Reversing a discount

$80 after 20% off was $100 (80 ÷ 0.8), not $96. You cannot add the discount back onto the smaller number.

Percent vs percentage points

4% to 5% is +1 point but +25% relative. Say which you mean.

Change is not symmetric

50 to 150 is +200%, but 150 to 50 is only −66.6667%. Use percentage difference when neither number is the starting point.

Adding successive percentages

10% off then 20% off is 100 → 9072: 28% off, not 30%. Multiply the factors 0.9 × 0.8.

Questions people ask

Percentage Calculator: frequently asked questions

How do I calculate a percentage of a number?

Convert the percentage to a decimal by dividing by 100, then multiply by the base number. For example, 20% of 150 is 150 × 0.20 = 30.

How do I find what percent one number is of another?

Divide the part value by the whole value, then multiply by 100. For example, 30 ÷ 150 × 100 = 20%.

How do I calculate percentage change?

Subtract the original value from the new value, divide by the absolute original value, then multiply by 100. The sign shows increase or decrease.

Why does the base number matter in percentage questions?

A percentage is always tied to a base or denominator. Changing the base changes the real amount even when the percentage number stays the same.

What should I print for a percentage worksheet or quote note?

Print the percentage, base number, applied amount, part and whole values, percentage-change baseline, formula, assumptions, date, page URL and notes area.

Why is a 50% increase followed by a 50% decrease not back to the start?

Because the second percentage is taken of a bigger number. 100 up 50% is 150; 50% of 150 is 75, so you end at 75, not 100. Likewise 100 down 20% is 80, and up 20% from there is 96.

What is the difference between percent and percentage points?

Percentage points subtract two percentages; percent compares them. A rate rising from 4% to 5% is 1 percentage point, which is a 25% increase in relative terms. Mixing them up is the most common mistake in news reports about rates and polls.

How do I find the original price after a discount?

Divide by what remains, not add the discount back. If $80 is the price after 20% off, the original is 80 ÷ 0.80 = $100. Adding 20% to $80 gives $96, which is wrong because 20% of the larger original is a bigger amount.

How do I add several percentages together?

Successive percentages multiply; they do not add. 10% off then 20% off leaves 100 → 90 → 72, a 28% total reduction, not 30%.

What is the difference between percentage change and percentage difference?

Percentage change has a direction and a starting point: 50 to 150 is +200%, but 150 to 50 is −66.6667%. Percentage difference has no direction and uses the average as the base, so 50 and 150 differ by 100% whichever order you say them. Use change for before-and-after, difference for two things compared side by side.

How do I calculate a percentage in my head?

Find 10% by moving the decimal one place left, then build: 5% is half of that, 15% is 10% + 5%, 20% is double 10%, and 1% is two places left. 15% of 48: 10% is 4.8, 5% is 2.4, so 7.2.

Can a percentage be more than 100%?

Yes. 150% of a number is one and a half times it. A percentage change above 100% means the value more than doubled. A percentage of a whole above 100% means you have more than the whole you started with.

Certification notes

Source, method and limitation basis

Percentage arithmetic is simple but easy to misread when the base is hidden. A strong percentage record says whether the number is an applied amount, a part of a whole or a change from an original baseline. Reviewed 2026-09-21.

Model limits

Straightforward percentage arithmetic on the numbers you enter. Percentage change uses the absolute value of the starting number as the base, which is the usual convention but is ambiguous for negative starting values. Percentage difference uses the average of the two absolute values. Results are shown to four decimal places.

Assumptions

  • A percentage is a fraction of 100, so 25% = 0.25 = 1/4.
  • Percentage change is measured from the starting value; it is not symmetric.
  • Percentage difference is measured against the average and is symmetric.
  • A starting value or whole of zero has no percentage and is reported as such.
  • Successive percentage changes multiply; they do not add.

Cite this page

Use the canonical URL, the page title “Percentage Calculator - CalculationTime”, and the review date 2026-09-21.