Percentage Calculator
Updated on September 29, 2026
Brighterly’s free percentage calculator solves every common percent problem in one place — find the percentage of a number, work out what percent one number is of another, calculate percent increase or decrease, find the whole from a part, and compare two values with percent difference or percent change.
Pick a mode, enter your numbers, and get an instant, accurate answer with the reasoning behind it — no guesswork, no manual formulas.
What is A% of B?
Step-by-Step Solution
Percentages Still Feel Tricky?
A free math assessment shows where your child needs support in just a few minutes. Grades 1–10.
What Is a Percentage?
A percentage is a way of expressing a number as a fraction of 100. The word itself comes from the Latin per centum, meaning “by the hundred.” Percentages let people compare proportions using one consistent scale, whether they’re looking at test scores, discounts, interest rates, or population growth.
| P% | P = the percentage (a ratio out of 100) |
|---|
For example, 25% means 25 out of every 100 parts, which is the same as the fraction 25/100 or the decimal 0.25. Percentages, fractions, and decimals are three ways of writing the same value — see our fraction calculator for how fractions convert into percentages, and our guide on how to teach percentages for classroom strategies by grade.
The Percentage Formula
Every percentage problem uses one core relationship between three values: the Part, the Whole, and the Percent.
| Part / Whole × 100 = Percent | The part divided by the whole, multiplied by 100, gives the percentage. |
|---|
This single formula can be rearranged to solve for any of the three values — which is exactly what the seven modes in the calculator above do.
How to Use the Percentage Calculator
Brighterly’s percentage calculator online is built to answer any percent question in a few clicks. Follow these steps:
| 1 | Choose a mode — select Percent of a Number, What Percent Is It?, Percent Change, Increase by %, Decrease by %, Find the Whole, or Percent Difference from the tabs at the top of the calculator. |
|---|---|
| 2 | Enter your numbers — type the values requested for that mode (for example, the Number and the Percent for “Increase by %”). |
| 3 | Click Calculate — the calculator instantly returns the result. |
| 4 | Review the formula — each mode is built on the same Part/Whole/Percent relationship, just solved for a different unknown. |
💡 Pro tip: If you’re not sure which mode you need, ask yourself what you already know and what you’re solving for — a part, a whole, or a percent. That answer points you straight to the right tab.
Percent of a Number
This is the most common percentage calculation: finding what a given percent of a number equals.
| Percent × Number = Result | Convert the percent to a decimal, then multiply. |
|---|
Example: What is 25% of 80? → 0.25 × 80 = 20
Example: What is 15% of 60? → 0.15 × 60 = 9
This is the calculation behind tips, sales tax, and test scores — “what is 20% of $45?” is exactly this formula.
What Percent Is It?
This mode answers: one number is what percent of another?
| (Part ÷ Whole) × 100 = Percent | Divide the part by the whole, then multiply by 100. |
|---|
Example: 20 is what percent of 80? → (20 ÷ 80) × 100 = 25%
Example: 9 is what percent of 60? → (9 ÷ 60) × 100 = 15%
This is the exact calculation used to turn a test score into a percentage — see our grades and test scores example below, and our fraction calculator guide for the fraction-to-percent link.
Find the Whole
This mode works backward from a part and a percent to find the original whole.
| Part ÷ Percent (as a decimal) = Whole | Divide the part by the percent, expressed as a decimal. |
|---|
Example: 20 is 25% of what number? → 20 ÷ 0.25 = 80
Example: 9 is 15% of what number? → 9 ÷ 0.15 = 60
This is useful when you know a discounted price and the discount rate, and need to find the original price.
Increase by % (Percentage Increase)
Increasing a number by a percentage means adding a percent of that number back onto itself.
| Number × (1 + Percent) = Result | Add the percent (as a decimal) to 1, then multiply by the number. |
|---|
Example: increase 80 by 25% → 80 × (1 + 0.25) = 80 × 1.25 = 100
Example: increase 500 by 10% → 500 × 1.10 = 550
This is the formula behind price markups, raises, and compound growth calculations.
Decrease by % (Percentage Decrease)
Decreasing a number by a percentage subtracts a percent of that number from itself.
| Number × (1 − Percent) = Result | Subtract the percent (as a decimal) from 1, then multiply by the number. |
|---|
Example: decrease 80 by 25% → 80 × (1 − 0.25) = 80 × 0.75 = 60
Example: decrease 500 by 10% → 500 × 0.90 = 450
This is the formula behind discounts, depreciation, and sale prices — “20% off $50” is a percentage decrease.
Percent Change (Percentage Increase or Decrease Between Two Values)
Percent change measures how much a value has grown or shrunk relative to its starting point. Unlike percent difference (below), percent change treats the two values asymmetrically — one is always the “before” and the other is the “after.”
| ((New − Old) ÷ Old) × 100 = Percent Change | Subtract old from new, divide by old, multiply by 100. A positive result is an increase; a negative result is a decrease. |
|---|
Example: a value goes from 80 to 100 → ((100 − 80) ÷ 80) × 100 = +25% (a 25% increase)
Example: a value goes from 100 to 80 → ((80 − 100) ÷ 100) × 100 = −20% (a 20% decrease)
Notice that increasing 80 by 25% gives 100, but decreasing 100 by 25% does not give back 80 — it gives 75. This asymmetry trips up many students; see common percentage mistakes below.
Percentage Difference
Percentage difference compares two values symmetrically — neither value is treated as the “original.” It’s used when there’s no natural before-and-after, just two quantities being compared.
| (|V1 − V2| ÷ ((V1 + V2) ÷ 2)) × 100 = Percentage Difference | Take the absolute difference, divide by the average of the two values, multiply by 100. |
|---|
Example: compare 10 and 6 → |10 − 6| ÷ ((10 + 6) ÷ 2) × 100 = 4 ÷ 8 × 100 = 50%
Use percent change when one value is clearly the starting point (like last year’s sales vs. this year’s). Use percentage difference when comparing two independent measurements (like two students’ scores, or two competing prices) with no “before.”
Percentage Formulas: Quick-Reference Table
| What You Know | What You’re Finding | Formula |
|---|---|---|
| Percent and Number | Part | Percent × Number |
| Part and Whole | Percent | (Part ÷ Whole) × 100 |
| Part and Percent | Whole | Part ÷ Percent (decimal) |
| Number and Percent | Increased Result | Number × (1 + Percent) |
| Number and Percent | Decreased Result | Number × (1 − Percent) |
| Old and New Value | Percent Change | ((New − Old) ÷ Old) × 100 |
| Two Values (no order) | Percentage Difference | (|V1 − V2| ÷ Average) × 100 |
Real-Life Examples of Percentage Calculations
Percentages appear constantly in everyday decisions — from shopping to grades to household budgeting. Here are four situations that come up most often.
Grades and Test Scores
A student answers 24 out of 30 questions correctly. Using “What Percent Is It?”: (24 ÷ 30) × 100 = 80%. This is the same relationship taught alongside fractions — see how fractions convert to percentages.
Shopping Discounts
A $50 jacket is 20% off. Using “Decrease by %”: 50 × (1 − 0.20) = $40. To check the discount amount alone, use “Percent of a Number”: 20% of $50 = $10 off.
Tips and Sales Tax
A $45 restaurant bill with an 18% tip: use “Percent of a Number” — 18% of 45 = $8.10 tip, for a total of $53.10.
Tracking Growth Over Time
A small business had 80 customers last year and 100 this year. Using “Percent Change”: ((100 − 80) ÷ 80) × 100 = +25% growth year over year.
Math Program CTA: Percentages Mastered. Ratios and Proportions Are Next. School pushes kids forward. Brighterly makes sure they’re ready — with 1:1 tutoring aligned to US state standards. [Book a Free Lesson]
Common Percentage Mistakes and How to Fix Them
These errors show up in student and adult work alike. Catching them early prevents costly real-world mistakes, from misread discounts to miscalculated grades.
| ❌ Common Mistake | ✅ Fix |
|---|---|
| Assuming a 25% increase and a 25% decrease cancel out | They don’t — the base number changes. Increasing 80 by 25% gives 100; decreasing 100 by 25% gives 75, not 80. |
| Forgetting to convert the percent to a decimal before multiplying | Always divide the percent by 100 first (25% → 0.25) before multiplying or adding to 1. |
| Confusing percent change with percentage difference | Use percent change when there’s a clear “before” and “after.” Use percentage difference for two independent values with no order. |
| Dividing by the wrong number when finding “what percent” | The number after “of” is always the whole (the denominator); the other number is the part. |
| Adding percentages directly instead of recalculating from the new base | A 10% raise followed by a 10% cut does not return to the original salary — recalculate each step from the current value. |
Percentages by Grade Level: What Students Learn and When
The progression below follows the US Common Core State Standards for Mathematics (CCSS). Percentage understanding builds directly on ratios, fractions, and decimals from earlier grades.
| Grade | Key Percentage Skills (CCSS) | Standard |
|---|---|---|
| Grade 4–5 | Understand fractions and decimals as building blocks for percent; compare fraction and decimal values. | 4.NF, 5.NBT |
| Grade 6 | Understand percent as a rate per 100; find a percent of a quantity; solve percent problems. | 6.RP.3c |
| Grade 7 | Solve multi-step percent problems: percent increase/decrease, discounts, markups, tax, tips, simple interest. | 7.RP.3 |
| Grade 8+ | Apply percent reasoning in proportional relationships, compound interest, and statistics. | 8.EE, 8.SP |
Students in Grades 6–8 working through percent word problems, discounts, and percent change can get 1:1 support from Brighterly’s middle school math tutors, each lesson personalized to the exact gap a child has — not the class average.
Frequently Asked Questions
What Is a Percentage Calculator?
A percentage calculator is a free online tool that solves percent problems — finding a percent of a number, working out what percent one number is of another, calculating percent increase or decrease, finding the whole from a part, and comparing two values with percent change or percentage difference. Brighterly’s percentage calculator covers all seven of these calculations in one tool.
How Do You Calculate a Percentage of a Number?
Convert the percent to a decimal by dividing by 100, then multiply it by the number. For example, to find 25% of 80: 0.25 × 80 = 20. This is the most frequently used percentage formula, covering tips, discounts, and test scores.
How Do You Find What Percent One Number Is of Another?
Divide the part by the whole, then multiply by 100. For example, 20 is what percent of 80? (20 ÷ 80) × 100 = 25%. The number that follows “of” is always the whole.
What Is the Difference between Percent Change and Percentage Difference?
Percent change compares a “before” value to an “after” value and is calculated as ((New − Old) ÷ Old) × 100 — the result can be positive (increase) or negative (decrease). Percentage difference compares two values with no inherent order, dividing their absolute difference by their average. Use percent change for tracking something over time; use percentage difference for comparing two independent measurements.
How Do You Increase a Number by a Percentage?
Multiply the number by 1 plus the percent expressed as a decimal. For example, to increase 80 by 25%: 80 × (1 + 0.25) = 80 × 1.25 = 100. This formula is used for price markups, raises, and growth projections.
How Do You Decrease a Number by a Percentage?
Multiply the number by 1 minus the percent expressed as a decimal. For example, to decrease 80 by 25%: 80 × (1 − 0.25) = 80 × 0.75 = 60. This is the formula behind discounts and depreciation.
Why Doesn’t Increasing Then Decreasing by the Same Percentage Return the Original Number?
Because each percentage is calculated from a different base value. Increasing 80 by 25% gives 100. Decreasing that 100 by 25% gives 100 × 0.75 = 75 — not 80 — because the second calculation is based on 100, not the original 80. This is one of the most common percentage misconceptions.
How Do You Find the Whole When You Know a Part and a Percent?
Divide the part by the percent, expressed as a decimal. For example, if 20 is 25% of a number, the number is 20 ÷ 0.25 = 80. This is useful for working backward from a discounted price to the original price.
How Are Percentages Related to Fractions and Decimals?
Percentages, fractions, and decimals are three ways of expressing the same ratio. To convert a percentage to a decimal, divide by 100 (25% = 0.25). To convert a decimal to a fraction, write it over a power of 10 and simplify (0.25 = 25/100 = 1/4). See Brighterly’s fraction calculator for the fraction side of these conversions.
Start Solving Percentage Problems Right Now
School pushes kids forward. Brighterly makes sure they’re ready.
Whether you’re checking a discount, calculating a grade, or working through a percent word problem, Brighterly’s percentage calculator gives an instant, accurate answer for every common percent question. Pair the calculator with related tools: the fraction calculator for fraction-to-percent conversions, and our guide on how to teach percentages for classroom strategies by grade.
When the calculator isn’t enough — when a child needs to really understand percentages, not just check them — Brighterly’s online math tutors are ready. Plans start from $17.70 per 45-minute lesson (12-month plan, 2 lessons/week, 20% discount applied).
Math & reading from 1st to 12th grade
Looking for homework support for your child?
Choose kid's grade
Math & Reading for Grades 1–12
Build real confidence for your child with a Brighterly math or reading tutor.
