On This Page
- Five questions, five modes
- Part, whole and percent
- Change or difference: which to use
- Going backward, and why rises do not cancel falls
- Discounts, stacked discounts and points
- Percentages in Excel
- How the five modes are verified
- FAQ
Five Questions, Five Modes
Pick the question from the dropdown, enter two numbers and read the answer with its working:
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | X ÷ 100 × Y | 15% of 80 = 12 |
| X is what % of Y? | X ÷ Y × 100 | 42 of 56 = 75% |
| % change from X to Y | (Y − X) ÷ |X| × 100 | $85,000 to $71,400 = −16% |
| % difference of X and Y | |X − Y| ÷ average × 100 | 48.2 and 51.6 = 6.81% |
| X% off Y | Y × (1 − X ÷ 100) | 35% off $280 = $182 |
The first mode also shows the number raised and lowered by that percentage, which is handy for tips and tax.
Part, Whole and Percent
"Percent" means "out of a hundred," so every one of these problems is the same relationship with a different unknown:
The hard part is spotting which number is the whole. A test score of 47 out of 60 is 47 ÷ 60 × 100 = 78.3%. An 8.5% tax on $240 is 0.085 × 240 = $20.40. A 3% commission on a $250,000 home is $7,500, and average real estate commission rates shows how that gets split.
Mental shortcut: 10% is the number divided by 10. Double it for 20%, halve it for 5%, add them for 15%. A 20% tip on $47 is $4.70 × 2 = $9.40. On a handheld calculator, 80 × 15 % gives 12 because the key does the ÷ 100 for you.
Very small percentages are easier to read in scientific notation: 0.0003% is 0.000003 as a decimal, or 3 × 10−6. The Scientific Notation Calculator converts these, and scientific notation practice problems has more like it.
Change or Difference: Which to Use
Use percentage change when one value came first, such as last quarter against this quarter. The original value is the base, and the calculator divides by its absolute value so negative starting numbers work too. Use percentage difference when neither value is the original, such as two stores' prices or two instrument readings. It divides by the average instead.
The choice changes the answer. $50 against $75 is a 50% rise one way, a 33.3% fall the other, and a 40% difference with no direction. Entering 80 and 120 gives 50% as a change but 40% as a difference.
Going Backward, and Why Rises Do Not Cancel Falls
To find the value before a change, divide by the multiplier: $96 after a 20% rise was $96 ÷ 1.20 = $80, and $170 after a 15% fall was $170 ÷ 0.85 = $200. The Markup Calculator and Profit Margin Calculator use the same reverse logic for pricing. For raises and pay, a 7% rise on $52,000 is $3,640, taking it to $55,640, and the Work Hours Calculator handles the hours side.
Always divide a change by the original value. Dividing by the new value is the most common mistake, and it is why a 20% fall followed by a 20% rise leaves you below where you started.
Discounts, Stacked Discounts and Points
A $120 jacket at 25% off costs $120 × 0.75 = $90. Going back, $90 ÷ 0.75 = $120, which is a quick way to check a "was/now" label. Stacked discounts multiply rather than add: 20% off and then 10% more leaves $100 × 0.80 × 0.90 = $72, a 28% total discount, not 30%.
Percentage points are a different measure again. A rate rising from 2% to 3% is up 1 percentage point but 50% in relative terms. Percentage points vs percent change covers when to use each.
Percentages in Excel
- X% of Y (A1, B1):
=(A1/100)*B1, or=A1*B1if A1 is formatted as a percentage. - A as a % of B:
=A1/B1with the cell formatted as a percentage. - % change:
=(B1-A1)/ABS(A1). Lock a fixed baseline with$B$1before filling down. - % difference:
=ABS(A1-B1)/((A1+B1)/2) - Apply a rate from B1:
=A1*(1+B1/100)for a rise,=A1*(1-B1/100)for a fall.
Percentage formatting multiplies by 100 only for display, which is why an unformatted cell shows 0.25 instead of 25%.
How the Five Modes Are Verified
Percent change divides the difference by the absolute value of the starting number, while percent difference divides the same-looking difference by the average of both numbers: entering 80 and 120 returns 50% from percent change but 40% from percent difference, because one formula treats 80 as the fixed reference point and the other treats both numbers as equals. The percent-of panel also computes two numbers nobody asked for directly, the base value plus and minus the entered percentage, and displays them alongside the main result as a quick reference. All five modes are separate branches in the same calculate() function, each reading only its own pair of input fields and clearing the display when either one is empty.
Frequently Asked Questions
How do you calculate percentage error?
Percentage error compares a measured or estimated value to a known or theoretical value: ((|measured − actual|) ÷ actual) × 100. A measurement of 48 cm against a true value of 50 cm: ((|48 − 50|) ÷ 50) × 100 = (2 ÷ 50) × 100 = 4% error. This is common in science labs and quality control checks.
How do you calculate profit percentage?
Profit percentage is profit divided by cost (or revenue, depending on whether you want gross margin or markup), multiplied by 100. Profit as a percentage of cost: ((selling price − cost) ÷ cost) × 100. Buy for $40, sell for $50: ((50 − 40) ÷ 40) × 100 = 25% profit on cost. For margin as a percentage of revenue: ((50 − 40) ÷ 50) × 100 = 20% margin. The Profit Margin Calculator and ROI Calculator both build on this same percentage arithmetic.
How do you calculate grade percentage?
Divide total points earned by total points possible, then multiply by 100. Earned 347 points out of 400: (347 ÷ 400) × 100 = 86.75%. For weighted grades, multiply each score by its weight, sum the weighted scores, then divide by the sum of all weights. The GPA Calculator handles the credit-weighted version of this automatically for course grades, and what GPA you need this semester to raise your cumulative GPA covers the reverse question, working backwards from a target.
References
- Khan Academy: Percent Word Problems: worked examples and practice for the core percentage formulas used in this calculator.
- Microsoft Support: Calculate percentages in Excel: official documentation for the Excel formulas referenced in the percentage-in-Excel section above.
- NIST: SI Units and Quantities: background on dimensionless quantities including percentage and how they are formally defined in measurement standards.