Percentage Calculator Quick Answer
Built and tested by the Mathvelo team · Last updated: October 2026 · Every worked example here was recomputed with exact arithmetic before publishing.
A percentage calculator turns “what is 15% of 240?” into one number: 36. The rule is percent ÷ 100 × whole. It also reverses the question: 36 is 15% of 240, and 36 out of 240 is 15%. Pick the question that matches your problem and type the two numbers you know.
How to Use This Percentage Calculator
- Choose the question. Percent of, what percent, percentage change, reverse percentage or discount.
- Enter the two numbers you know. The calculator labels each box, so you cannot mix up the part and the whole.
- Read the formula line. It prints the formula with your numbers filled in, then the answer.
| Question | Formula | Example |
|---|---|---|
| What is x% of y? | x ÷ 100 × y | 15% of 240 = 36 |
| What percent is a of b? | a ÷ b × 100 | 36 of 240 = 15% |
| Percentage change | (new − old) ÷ old × 100 | 80 → 100 = +25% |
| Percentage difference | |a − b| ÷ average × 100 | 40 vs 60 = 40% |
| Reverse percentage | final ÷ (1 ± rate) | $60 after 20% off = $75 |
| Ask in words | Reads a typed question | 35% of 80 = 28 |
How to Calculate a Percentage of a Number
“Percent” means per hundred, so 15% is 15/100 = 0.15. Multiply the whole by that decimal. A faster mental route is the ten-percent block: 10% of 240 is 24, 5% is half of that, 12, and 15% is 24 + 12 = 36.
Percentage Increase and Decrease
Percentage change is the change divided by the starting value. Going from 80 to 100 is +20 on a base of 80, so +25%. Going from 120 down to 90 is −30 on a base of 120, so −25%. The sign tells you the direction.
Start with 100
- +20% gives 100 × 1.20 = 120.
- −20% of 120 is 24, so 120 × 0.80 = 96.
- The second percent was taken from a larger base, so the total falls by 4%.
Answer: 96, a net change of −4%
Percentage Change vs Percentage Difference vs Percentage Points
Percent change compares a new value with an old one. Percentage difference compares two values with no “old”, so it divides by their average: 40 and 60 differ by 20 ÷ 50 = 40%, while 40 to 60 is a 50% increase. Percentage points subtract two percentages: a rate rising from 4% to 6% is 2 percentage points, or a 50% relative increase. News headlines mix these up constantly.
Reverse Percentages: Find the Original Price
Ask “percent of what?” before typing anything. A price after 20% off is 80% of the original, so divide, never add back: $60 ÷ 0.80 = $75. Adding 20% to $60 gives $72, which is wrong because the 20% was taken from $75. With tax it is the same idea: a $108.50 total at 8.5% tax came from $108.50 ÷ 1.085 = $100.
Discount, Sales Tax, Tip and Markup
- Discount then tax: 20% off with 8.5% tax is 0.80 × 1.085 = 0.868, which is 13.2% off, not 11.5%.
- Tip: 18% of $64.50 is 0.18 × 64.50 = $11.61.
- Markup vs margin: cost $60, sell $80. Markup is 20 ÷ 60 = 33.3%; margin is 20 ÷ 80 = 25%. Same profit, different base.
- Compound growth: $1,000 at 5% for 10 years is 1,000 × 1.05¹⁰ = $1,628.89, against $1,500 with simple interest. The logarithm calculator solves for the number of years.
Grades, Averages, Weight Loss and Percent by Mass
A grade is a percentage of marks: 43 out of 50 is 43 ÷ 50 × 100 = 86%. A weighted average multiplies each score by its weight: an exam worth 60% scoring 80 and coursework worth 40% scoring 90 gives 0.6 × 80 + 0.4 × 90 = 84. Do not average the 80 and 90 straight, because the exam counts for more.
Weight loss uses the same change formula: from 90 kg to 81 kg is −9 ÷ 90 = −10%. In chemistry, percent by mass is the part’s mass divided by the total: 5 g of salt in 95 g of water makes 5 ÷ 100 = 5% salt, because the total is 100 g, not 95 g.
Simple Interest, Compound Interest and CAGR
Simple interest pays on the original amount only: $1,000 at 5% for 10 years earns $50 a year, $500 in total. Compound interest pays on the growing balance, so the same deposit reaches 1,000 × 1.05¹⁰ = $1,628.89. To go the other way, the compound annual growth rate (CAGR) is (end ÷ start)^(1 ÷ years) − 1. From $1,000 to $1,628.89 over 10 years that returns 5%, which is a useful way to compare investments of different lengths.
How to Do Percentages on a Phone or Calculator
Most phone calculators treat the % key differently from a desk calculator, and that is a common source of wrong answers. On a phone, typing 240 × 15 % usually gives 36, but 240 + 15 % may give 276, because it adds 15% of 240. A desk calculator can do the opposite. Avoid the key: type 240 × 0.15 for a percent of, or 240 × 1.15 for an increase, and 240 × 0.85 for a decrease. The calculator on this page shows the formula, so you can see which route it took.
Our Take: What Is Overrated, Underrated and Plain Wrong
Overrated: percentage-point and percent being the same thing. A rise from 4% to 6% is 2 percentage points but a 50% increase.
Underrated: working backwards with the reverse formula. It undoes discounts and tax cleanly.
Plain wrong: adding a 20% discount and a 10% discount to get 30% off. Applied one after the other they give 28% off.
Percentage Practice Problems With Answers
Try each by hand first.
- What is 35% of 80?
Answer
28 - Percent change from 80 to 100?
Answer
+25% - A coat costs $60 after 20% off. Original price?
Answer
$75 - Percentage difference between 40 and 60?
Answer
40% - A price rises 10% then falls 10%. Net change?
Answer
−1%
Written by the Mathvelo team, who do not claim a teaching credential. Every method is shown so you can check it. See About, Contact, Privacy and Terms, or report a mistake.
Why Students Get Stuck on Percentages, and What a Good Calculator Should Do
Searching for help with percentages usually starts late at night with one problem that will not work out. "percent of", "percent change" and "percentage points" are different questions. A good calculator fixes that by showing each step, checking its own answer and explaining the idea in plain words. This section covers what students struggle with, what they want, and how this page responds.
In short: students need to choose the right formula and read the answer correctly, not just see a final number, and a calculator earns trust only when its steps can be checked.
Understand the pain points
What students get stuck on
Most mistakes here are not about arithmetic. They come from one rule applied the wrong way round, which is why seeing every step matters.
- Mixing up the base in percent changeWhat is 15% of 240?↗
- Adding and subtracting percentages directlyIncrease 50 by 20%↗
- Confusing percent with percentage pointsPercent change from 80 to 100↗
- Not converting between percent and decimal
Understand the frustrations and desires
What they feel, and what they want
Each frustration points to a wish: a clearer step, a built-in check, an explanation in plain words.
- Wants the right formula named
- Wants increase and decrease shown clearly
- Wants the answer in words
Build the page around their intent
Each intent has a place on this page
The page follows intent, not features, so each need has a clear starting point.
- I need an answer now: type the problem into the calculator at the top of this page.What is 15% of 240?↗
- I need to understand: the sections below explain the idea in plain words and list the common mistakes.
- I need to check my work: every step is shown, so the first line that differs from yours is the one to study.
- I need practice: open the solver, tap + and choose Create Practice Test.
- I need it explained aloud: in the solver, tap + and choose Create Video.