Why direction matters
Going from 80 to 100 rises by 25%. Going from 100 back to 80 falls by 20%. The difference is still 20, but the starting value changes.
Free Online Percentage Calculator
Calculate tips, discounts, markups, grades, and percentage changes.
Your result
Your answer will appear here.
Worked examples & guides Open one when you want more detail.
THE MATH, MADE SIMPLE
How much did it increase or decrease?
Enter an original value and a new value to find the percentage increase or decrease and the absolute change. The same difference can mean something very different depending on where you begin.
FOR A POSITIVE STARTING VALUE
New − OriginalOriginal
× 100WORKED EXAMPLE · 80 TO 100
A change of 20. An increase of 25%.
For an old price of 80 and a new price of 100, subtract the original value from the new value: 100 − 80 = 20. Divide that change by the original 80, then multiply by 100.
(100 − 80) ÷ 80 × 100 = 25%
These are example numbers. Your own calculation and formula appear in the calculator’s result above.
Percent vs. percentage points
A grade going from 80% to 90% rises by 10 percentage points. Relative to the original 80%, that’s a 12.5% increase: (90 − 80) ÷ 80 × 100. Enter 80 and 90 to find that relative change. Percentage points and relative percentage change are different measurements.
Zero and negative values
A zero original has no defined percentage change, even from 0 to 0. For a negative original, divide by its magnitude: −100 to −50 is a 50% upward movement. This is a magnitude-based convention, not a standard growth rate. Interpret crossing zero carefully.
Recovering from a percentage loss
A 20% loss takes 100 to 80. Recovering the missing 20 requires 20 ÷ 80 × 100 = 25% growth. For a loss of L% below 100%, the recovery percentage is L ÷ (100 − L) × 100. A 50% loss needs a 100% gain; a 100% loss leaves zero, so percentage growth from that zero base is undefined. Use 80 as Original and 100 as New to check the 25% recovery.
Understanding the absolute change
Absolute change here means the signed difference, new minus original. A positive result moves upward; a negative result moves downward. Equal values have zero difference and, for a nonzero original, 0% change. Compare numbers in matching units. Results are approximate and rounded; very small or large values use scientific notation.
THE MATH, MADE SIMPLE
A percentage turns a number into an amount.
Choose Percentage of a number from the calculator menu when you know the rate and want the amount it represents. Use it for a proportion of a quantity. Tip and Discount have their own dedicated calculators for amounts and totals. It does not add or subtract that amount from the original.
PERCENTAGE AMOUNT
Number × Percentage100
WORKED EXAMPLE · 25% OF 80
The amount is 20.
First divide 25 by 100 to get 0.25. Multiply 80 by 0.25 to get 20. For example, one quarter of a quantity of 80 is 20, leaving 60. This matches the example button in this calculator.
80 × 25 ÷ 100 = 20
You can check the example by dividing back: 20 ÷ 80 × 100 = 25%. The result shows your amount; How it’s calculated explains the formula.
Enter the rate as a percent
Type 25 for 25%, not 0.25. Entering 0.25 calculates one quarter of one percent. Use the same unit for the original number and the resulting amount.
Above 100% and zero
150% of 80 is 120: percentages can exceed the original number. 0% of any supported number is zero, and every finite percentage of zero is zero.
Signed multiplication
20% of −100 is −20. This mode keeps both signs in the multiplication. Increase / decrease instead uses a negative starting value’s magnitude so its Increase and Decrease controls have consistent directions.
THE MATH, MADE SIMPLE
Choose the whole before finding the share.
Choose Part as a percentage from the calculator menu when you know the part and the reference whole. Use it for completed items out of a total, points earned out of available points, or an amount compared with a target. Put the reference total in Whole and use matching units.
PART AS A PERCENTAGE
PartWhole
× 100WORKED EXAMPLE · 20 OUT OF 80
20 is 25% of 80.
Divide 20 by 80 to get 0.25, then multiply by 100. If 20 of 80 items are complete, 60 remain: that is the other 75%. This matches the calculator’s example. You can check it by reconstructing the part.
20 ÷ 80 × 100 = 25%
80 × 25 ÷ 100 = 20. Rounding a repeating percentage may make the displayed check approximate; calculations use the unrounded values.
A share is different from a change
20 is 25% of 80, but going from 80 to 20 is a 75% decrease. The first question compares the part with the whole; the second compares the difference with the starting value. Use Percentage change for the second question.
A part can exceed the whole
30 out of a target of 24 is 125%. A result above 100% can describe exceeding a target. A zero part with a nonzero whole gives 0%; a zero whole is undefined, including 0 out of 0.
Negative values are signed ratios
A negative part divided by a positive whole produces a negative percentage. Two negative inputs produce a positive ratio. These are algebraic comparisons, not conventional shares of a positive total.
THE MATH, MADE SIMPLE
One percentage. Two useful numbers.
Enter a starting value and a percentage, then choose Increase or Decrease. Multiply the starting magnitude by the percentage, then add or subtract that amount to get the new value.
CHANGE AMOUNT
|Starting value| × Percentage100
WORKED EXAMPLE · 80 WITH A 25% INCREASE
A change amount of 20. A new value of 100.
25% of 80 is 20. Add that amount to the starting value for Increase, or subtract it for Decrease.
80 × 25 ÷ 100 = 20
Increase80 + 20 = 100
Decrease80 − 20 = 60
These are example numbers. Your own change amount, new value, and formula appear in the calculator’s result above.
Why reversing a change differs
A 25% increase takes 80 to 100. A 25% decrease from 100 gives 75, not 80, because the percentage now uses a different starting value. A 20% decrease from 100 returns to 80.
Percent vs. percentage points
Applying a 50% increase to a rate of 10% gives 15%. That is a rise of 5 percentage points. Enter 10 as the starting value and 50 as the percentage; entering 5 would apply a 5% relative increase instead.
Zero and negative starting values
Any percentage of zero is zero, so a zero start stays zero. For a negative start, use its magnitude: 50% of |−100| is 50. Increase adds 50 to give −50; Decrease subtracts 50 to give −150. Increase always moves upward and Decrease downward, unless the amount is zero.
Zero, negative, and large percentages
A 0% adjustment leaves the starting value unchanged. Enter a percentage of zero or more and use the direction selector rather than a negative percentage. Percentages above 100 are allowed: a 150% decrease from 80 subtracts 120, giving −40. The change amount is a magnitude, with its Added or Subtracted label showing the direction. Values are unit-neutral; results are approximate and rounded.
Enter the bill amount you want to base the tip on and your chosen tip percentage. For a bill of 60 and a 20% tip, the tip is 12 and the total bill is 72. Use the same currency throughout; the calculator does not convert currencies.
Choose whether your bill amount includes tax before entering it. Check for an existing service charge. This calculator adds only your chosen tip, not separate taxes or fees. A zero tip leaves the bill unchanged.
Tip first, then split the total
For a 60 bill and 20% tip: 60 × 20 ÷ 100 = 12; 60 + 12 = 72. Split equally between three people, that is 72 ÷ 3 = 24 each. This tool calculates the tip and total; divide the total separately to split it. If people owe different shares, an equal split will not reflect their individual orders.
Check the base and existing charges
If 60 is the pre-tax amount and tax is 6, tipping 20% on 60 gives 12, while tipping on 66 gives 13.20. Enter the base you intend to use; add any tax omitted from that base separately. A service charge is not always a gratuity—check the bill or ask the business before adding another tip. Results are not automatically rounded to cents: round the final payable amount according to your currency and payment rules.
Subtract a discount from the original price
Enter the original price first. Then type either the percentage or the dollar amount; the other box updates automatically. Changing the original price keeps the last field you edited and updates its partner.
For an original price of $80, enter 25%. The linked dollar amount becomes $20.
$80 × 25 ÷ 100 = $20
$80 − $20 = $60 final price
A discount subtracts the amount. It cannot exceed the original price or 100%. A full 100% discount makes the price zero.
A percentage of a zero original price gives an amount of $0. A dollar amount cannot determine a percentage of zero; that percentage stays undefined. A dollar markup on $0 can still produce a final price. Linked values are rounded for display, while calculations keep using the last value you typed. Tax and fees are not included.
Two 20% discounts save 36%, not 40%
Start at $100. The first 20% discount leaves $80; the second takes 20% of $80 ($16), leaving $64. Total savings are $36, or 36% of the original price. For successive discounts a and b, the remaining fraction is (1 − a/100) × (1 − b/100). Use the discounted price as the original price for the next calculation. Store rules may exclude coupon stacking.
Markup and margin use different bases
Buying for $80 and selling for $100 earns $20 before other costs. Markup uses cost: $20 ÷ $80 × 100 = 25%. Margin uses selling price: $20 ÷ $100 × 100 = 20%. Choose Markup here to add 25% to $80 and get $100. For a target 25% margin, selling price = $80 ÷ (1 − 0.25) ≈ $106.67; adding 25% would miss that target. Use Part as a percentage to compare profit with selling price. These calculations exclude overhead, tax and fees.
Recover the original price
If a price after a 20% discount is $64, the original was $64 ÷ 0.80 = $80. Adding 20% to $64 gives $76.80 because it uses the smaller base. Divide by the fraction remaining; a 100% discount leaves zero and cannot reveal the original price.
Divide points earned by points possible, then multiply by 100. Earning 18 out of 20 points gives 90%. Possible points must be greater than zero. Extra credit can produce a percentage above 100%.
This gives a single percentage score. It does not assign a letter grade or calculate a weighted course grade. Use your school’s grading rules for those decisions.
Unequal point totals: combine points first
Suppose you earn 18/20 on a quiz (90%) and 70/100 on an exam (70%). If the course uses total points, enter earned points 88 and possible points 120: 88 ÷ 120 × 100 ≈ 73.3333%. Averaging 90 and 70 gives 80%, which incorrectly treats the 20-point quiz like the 100-point exam.
Category weights: a different calculation
If quizzes count for 30% and exams for 70%, a quiz average of 90% and exam average of 70% give 90 × 0.30 + 70 × 0.70 = 76%. That is a weighted average, not the total-points score above. This calculator accepts earned and possible points only; it does not apply category weights. Follow the syllabus for missing work, dropped scores, rounding and extra credit. Incomplete category weights need an explicit policy; do not treat ungraded work as zero unless required.
The arithmetic mean is the sum divided by the number of entries. For 10, 20, 30, the sum is 60 and the average is 20. Negative numbers, decimals, zero and a single number are supported. Enter up to 1,000 numbers, separated by commas or new lines.
Commas separate entries, so type 1000 for one thousand. Every entry has equal weight. An average of assignment percentages is not necessarily a course grade when assignments have different weights or possible points. Use values with matching units.
Simple average or weighted average?
If two equal-size groups average 10 and 20, their combined average is 15. If the first group has 2 people and the second has 8, the combined average is (10 × 2 + 20 × 8) ÷ (2 + 8) = 18. Typing just 10, 20 here gives 15 because each entry counts once. This tool does not accept a separate weight field; calculate weighted totals and divide by the total weight separately.
Do not average percentages blindly
18/20 and 70/100 are 90% and 70%, but their combined points percentage is 88/120 ≈ 73.3333%, not the simple mean of 80%. Use Grade with the summed points for that question. For a simple average, include real zeros (10, 0, 20 averages 10) and omit missing observations only when your measurement policy calls for it. An unusually large value can pull the mean away from a typical observation; the mean is not the median.
About Percentage Tool
Percentage Tool is operated by Chris Holcomb.
Work out a tip and total bill, a discount or markup and final price, a percentage score, or the average of a list. Percentage change compares an original and new value. The calculator menu also includes increase or decrease, percentage of a number, and part as a percentage. Each result includes a short explanation and optional calculation details. Use this free online percentage calculator with numbers in any matching units. It runs in your browser with no download, installation, or account needed. Absolute change here means the signed difference, new minus original; its size is the distance between the values.
Results are approximate and rounded for readability. Very small or large results use scientific notation. Compare values in matching units and use the context to interpret the result.
Privacy
Last updated September 8, 2026.
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