Percentage Calculator

A percentage is just a fraction of 100 - the word literally means "per hundred." This percentage calculator handles the three questions people ask most: what is a percent of a number, what percent one number is of another, and how much something changed in percent terms. For example, 15% of 200 is 30: you turn 15% into the decimal 0.15 and multiply by 200. Switch the mode to ask the reverse - 45 is 25% of 180 - and the same numbers tell a different story.

The three core formulas

Every percentage problem reduces to one of these three relationships:

If you know two of the three quantities in any line, you can solve for the third. That is why a single tool can answer "what is 15% of 200," "45 is what percent of 180," and "what's the percent increase from 120 to 150" with the same underlying math.

Percent increase vs percent decrease

Percent change compares a new value to an original one. A positive result is an increase, a negative result is a decrease. Going from 120 to 150 is a +25% increase; going from 150 back to 120 is a −20% decrease. Notice the two are not symmetric: a 25% rise followed by a 25% fall does not return you to the start, because each percentage is taken against a different base. Always divide by the original value, not the new one.

Converting between percent, decimal and fraction

To use a percentage in a calculation, drop the % sign and divide by 100: 15% = 0.15 = 15/100 = 3/20. To go the other way, multiply a decimal by 100 and add a % sign: 0.075 becomes 7.5%. Keeping the decimal form in mind makes mental math faster - 10% of any number is just that number with the decimal point moved one place left, and 1% moves it two places.

Everyday uses

• Tips and discounts: 20% of a $45 bill is $9; a 30%-off $80 item saves $24.
• Grades and test scores: 45 correct out of 60 is 75%.
• Growth and decline: revenue from $120k to $150k is a 25% increase.
• Comparisons: express any "part of a total" as a clean percentage to compare fairly.

How to use this calculator

Each mode answers a different question, so the first step is picking the one that matches yours:

1. Choose the mode. Use "X% of Y" when you know the percentage and want the amount (a tip, a discount, a tax). Use "X is what percent of Y" when you have two amounts and want the percentage (a score, a market share). Use "percent change" when you are comparing a before and an after value.
2. Enter the two known numbers. Type plain numbers without the % sign or dollar sign - just the digits, with a decimal point if needed.
3. Read the result and the breakdown. The headline figure is your answer; the decimal/ratio line underneath shows the working so you can sanity-check it.
4. Read the answer sentence. A plain-English line restates the result ("45 is 25% of 180") so you can copy it straight into an email, report or homework answer.

A second worked example, step by step

Suppose a store cuts a $250 coat to $190 and you want to know the discount. Use percent change with the old value 250 and the new value 190:

• Find the difference: 190 − 250 = −60.
• Divide by the original: −60 ÷ 250 = −0.24.
• Multiply by 100: −0.24 × 100 = −24%.

The coat is 24% off. The negative sign simply means the value went down. To go the other way and confirm, take 24% off $250: 250 × (1 − 0.24) = 250 × 0.76 = $190. The two checks agree, which is a quick way to catch a mis-typed number.

Who this calculator is for

Percentages turn up far beyond math class, and this tool is built for everyday, non-specialist use:

• Shoppers working out sale prices, stacked discounts and sales tax before they reach the register.
• Students and parents converting raw scores into grades, or checking homework percentages.
• Diners splitting a check and adding a tip without the awkward mental math.
• Small-business owners and freelancers sizing margins, markups, commissions and month-over-month growth.
• Anyone reading the news who wants to sanity-check a "rose 40%" or "down by half" claim against the underlying numbers.

Key terms, in plain English

• Percent (%): a fraction out of 100. 37% means 37 out of every 100, or the decimal 0.37.
• Part and whole: the "part" is the smaller quantity you are measuring; the "whole" is the total it belongs to. In "45 out of 180," 45 is the part and 180 is the whole.
• Base value: the number a percentage is taken of. In percent change it is always the original (older) value - getting the base wrong is the most common mistake.
• Percentage point: the plain difference between two percentages. A move from 4% to 6% is 2 percentage points, which is a separate idea from the 50% relative change.
• Markup vs margin: markup is the increase over cost; margin is the profit as a share of the selling price. A $40 cost sold at $50 is a 25% markup but only a 20% margin - the two are not the same number.

Reversing a percentage to find the original

One of the most useful tricks is working backward from a value that already includes a change. If you know the result and the percentage, divide instead of multiply:

• Remove an increase: a price is $120 after a 20% rise, so the original was 120 ÷ 1.20 = $100.
• Remove a discount: a coat costs $90 after 25% off, so the list price was 90 ÷ 0.75 = $120.
• Strip out sales tax: a receipt total of $54 at 8% tax means the pre-tax price was 54 ÷ 1.08 = $50.

The mistake to avoid is taking the percentage off the final figure. Subtracting 20% from $120 gives $96, not $100, because the original 20% was calculated on the smaller starting number, not the larger final one.

Scenario comparison: the same numbers, three questions

One pair of numbers - say 30 and 200 - answers a completely different question depending on which mode you pick. Seeing all three side by side is the fastest way to understand what each mode actually does:

• 30% of 200 → (30 ÷ 100) × 200 = 60. Here 30 is a rate and 200 is the base; the answer is an amount.
• 30 is what percent of 200? → (30 ÷ 200) × 100 = 15%. Now 30 is a part and 200 is the whole; the answer is a rate.
• Percent change from 200 to 30 → ((30 − 200) ÷ 200) × 100 = −85%. Here 200 is the "before" and 30 is the "after"; the answer is a drop.

Same digits, three answers - 60, 15% and −85% - because the role each number plays changes. Getting fluent at spotting "is this number a rate, a part, or a starting value?" is most of what it takes to never reach for the wrong formula again.

Quick mental-math shortcuts

You rarely need a calculator for round percentages once you anchor on 10% and 1%. A few moves cover most everyday cases:

• 10%: move the decimal one place left. 10% of 340 is 34.
• 1%: move the decimal two places left. 1% of 340 is 3.40.
• 5%: take 10% and halve it. 5% of 340 is 17.
• 15% (a common tip): 10% plus half of that again. 15% of 340 is 34 + 17 = 51.
• 20%: double the 10% figure. 20% of 340 is 68.
• The swap trick: X% of Y equals Y% of X. 4% of 75 is hard, but 75% of 4 = 3 is instant.

For amounts that fall between these anchors, add the building blocks: 35% is 10% + 10% + 10% + 5%. When you do need an exact figure, the calculator above confirms your estimate in one tap, which is handy for sanity-checking a restaurant tip or a store discount on the spot.

What changes the result the most

If you change one input at a time and watch the answer move, a clear pattern emerges about which number matters in each mode:

• In "X% of Y": the result scales evenly with both inputs. Doubling either the percentage or the base doubles the answer, so a 1% slip in the rate moves the result by exactly 1% of the base.
• In "part is what % of whole": the whole is the lever that most distorts the answer. The same part of 100 vs. 1,000 gives 30% vs. 3% - a small whole makes the percentage swing wildly, which is why tiny sample sizes produce unreliable percentages.
• In percent change: the starting value drives everything, because it is the denominator. A change of 10 looks huge against a base of 20 (+50%) and trivial against a base of 2,000 (+0.5%).

The recurring theme is the denominator: in two of the three modes the bottom number does the heavy lifting, so identifying the correct base is more important than getting the top number exactly right.

Percentages in finance, statistics and grading

The same three formulas power most of the percentages you meet in real reports, even when they wear different names:

• Inflation and growth rates are percent change applied to an index or a revenue figure year over year - the Consumer Price Index, for instance, is reported as a percent change from twelve months earlier.
• Interest rates are a percent of a balance, though compounding (interest on interest) needs a dedicated tool once more than one period is involved.
• Market share, turnout and approval ratings are all "part is what percent of whole," which is why the size of the whole (the sample or electorate) decides how much weight a single point carries.
• Test scores and grades are "part is what percent of whole" too - points earned over points possible - and a weighted course grade is just a series of those percentages averaged with different multipliers. For a full course breakdown, a dedicated grade calculator or GPA calculator handles the weighting for you.

Recognising which of the three formulas a real-world figure came from makes it much easier to question or reproduce a statistic you read.

How this compares to related calculators

This page is the general-purpose tool for one-step percentages. When your question has a specific shape, a focused calculator gives a cleaner answer:

• For a before-and-after comparison framed only as a rise, use the Percentage Increase Calculator.
• For any signed before/after movement, up or down, use the Percentage Change Calculator.
• To take a percentage off a price and see the dollars saved, use the Discount Calculator.
• To add a percentage on top of a bill, use the Sales Tax Calculator or the Tip Calculator.
• To express a relationship as a clean A:B proportion rather than a percent, use the Ratio Calculator; to convert a percent into its fraction form, the Fraction Calculator helps.
• To find how far a measured value sits from an expected one, use the Percent Error Calculator.

Limitations and assumptions

This is a general-purpose arithmetic tool, so a few boundaries are worth knowing. It works on simple, one-step percentages - it does not compound a rate over multiple periods, so it is not a substitute for an interest or investment calculator. It rounds displayed results to two decimals for readability; if you are feeding figures into tax, payroll or grading systems, follow the exact rounding rule that system requires rather than the rounded value shown here. It also treats every input as a plain number with no units, so it cannot know whether you mean dollars, students or percentage points - that context is up to you. Finally, division by zero (a whole or starting value of 0) has no meaningful percentage, so the calculator flags those cases instead of inventing an answer.