Free Online Calculators That Show Their Work
Most calculator sites hand you a number and expect you to trust it. Every tool here shows the formula underneath, so you can check the answer — or work out how to do it yourself next time.
There are nineteen of them, covering the percentage, money and school questions people actually look up: what X% of Y is, what a sale price works out to, whether a raise beat inflation, how long a card balance takes to clear. Plus a full debt payoff planner that compares five strategies side by side.
All free, nothing to install, and no account needed to use any of it.
Debt Payoff Planner
Enter what you owe and see the actual date you'll be debt-free. It runs the real month-by-month math, compares five payoff strategies side by side so you can see what each one truly costs, and tracks your progress as you pay it down. No bank connection, no paywall.
Build my payoff plan →What is X% of Y?
Discount Calculator (X% off Y)
X is what percent of Y?
Percentage Increase / Decrease
Tip Calculator
Percentage Formulas Explained
Percentages are used everywhere — shopping, finance, school, statistics, and everyday comparisons. Here are the five formulas behind almost everything you'll ever need to calculate.
1. Basic Percentage Formula
Formula: (Part ÷ Whole) × 100
Use this whenever you know a part and a whole, and want to express the part as a percentage. It's the foundation every other formula on this page builds from.
Example: You got 15 out of 60 questions correct. (15 ÷ 60) × 100 = 25%.
2. Percent of a Number
Formula: (X ÷ 100) × Y
Use this to find what a given percentage of a number actually equals — like figuring out a discount or a tax amount before you add it in.
Example: 20% of a $50 bill. (20 ÷ 100) × 50 = $10.
3. What Percent Is X of Y?
Formula: (X ÷ Y) × 100
Use this when you have two numbers and want to know what percentage the first represents of the second — the reverse of the formula above.
Example: 12 is what percent of 40? (12 ÷ 40) × 100 = 30%.
4. Percentage Increase or Decrease
Formula: ((New − Old) ÷ Old) × 100
Use this to measure how much a value has grown or shrunk relative to its starting point — always divide by the original value, never the new one.
Example: Price rises from $40 to $50. ((50 − 40) ÷ 40) × 100 = 25% increase.
5. Tip Calculation Formula
Formula: (Tip % ÷ 100) × Bill
Use this to calculate a tip amount from a percentage and a bill total — the same structure as "percent of a number," applied to a restaurant check.
Example: 18% tip on a $60 bill. (18 ÷ 100) × 60 = $10.80.
Common Percentage Mistakes
Percentage math is simple in theory, but these five mistakes account for most of the errors people actually make.
1. Forgetting to Convert Percent to Decimal
25% = 0.25, not 25. Plugging the raw number 25 straight into a formula instead of 0.25 gives an answer 100 times too large.
Fix: Always divide the percent by 100 before multiplying — every formula on this page does this as its first step.
2. Dividing the Wrong Way
To find what percent X is of Y, divide X by Y — not Y by X. Flipping the division gives a completely different, usually much larger, number.
Fix: Correct formula is (Part ÷ Whole) × 100. The "part" always goes on top.
3. Mixing Up Increase and Decrease
Always divide by the original (starting) value, not the new one. Using the wrong base value silently changes the answer, especially on large swings.
Example: 40 → 50 is a 25% increase, but 50 → 40 is a 20% decrease — not the same percentage in reverse.
4. Adding Percentages Incorrectly
Stacked percentages don't simply add together. "25% off, then an extra 10% off" is not 35% off in total.
Example: $100 × 0.75 × 0.90 = $67.50 — a real discount of 32.5%, not 35%, since the second discount applies to the already-reduced price.
5. Forgetting That Percentages Are Relative
A jump from 10 to 20 is a 100% increase, not 10 — percentage change depends entirely on the starting value.
Example: Going from 10 to 20 doubles the value, which is a 100% increase, even though the raw difference is only 10.
Percentage Conversion Table
| Percentage | Decimal | Fraction |
|---|---|---|
| 1% | 0.01 | 1/100 |
| 5% | 0.05 | 1/20 |
| 10% | 0.10 | 1/10 |
| 25% | 0.25 | 1/4 |
| 50% | 0.50 | 1/2 |
| 75% | 0.75 | 3/4 |
| 100% | 1.00 | 1/1 |
The One-Line Version
Everything above comes back to a single idea: a percentage is a number expressed as a part of 100. Divide the part by the whole, multiply by 100, and you have it.
Percentage = (Part ÷ Whole) × 100
25% of 80 = 20 — because 0.25 × 80 = 20
45 out of 50 = 90% — because (45 ÷ 50) × 100 = 90
40 → 50 is a 25% increase — because the 10-point rise is measured against the 40 you started from, not the 50 you ended at
That last one is where most mistakes happen. The number you divide by is the number you started with, and getting that backwards is the single most common percentage error there is.
More Calculators
Looking for something more specific? Try one of these: