Percentage Calculator
Calculate discounts, markups, percentage differences, cross-multiplication (rule of three), and fractions instantly, with results rounded to 4 decimal places
Understanding Proportions and Percentages
A percentage is simply a ratio out of 100. Store discounts, sales tax and investment returns all come down to the same idea of proportion.
Three tools in one: the rule of three finds the fourth value of a proportion when three are known (A / B = C / X for direct; A × B = C × X for inverse), and the fractions mode turns a fraction into a decimal and a percentage.
Calculation Breakdown
How to use this tool
- Pick a mode: Percentages, Rule of Three or Fractions.
- In Percentages, choose the question type (for example “What is X% of Y?”) and fill in the two boxes.
- In Rule of Three, enter A and B (the known pair) plus C; in Fractions, enter numerator and denominator.
- Read the result, the formula applied, the decimal equivalent and the simplified fraction, then copy it if needed.
Worked example
Percentages: 15% of 250 is (15 ÷ 100) × 250 = 37.5, which is also 75/2 as a fraction. Rule of Three: if 5 items cost 100, then 8 items cost (100 × 8) ÷ 5 = 160. Fractions: 3/4 equals 0.75, or 75%. A typical everyday use is a tip or a discount: 15% off a 250 price removes 37.50, leaving 212.50.
Methodology
Everything here is elementary arithmetic. The rule of three rests on a basic property of proportions: the product of the extremes equals the product of the means (a · d = b · c).
Five slips that make a percentage look right but wrong
These are the mix-ups that produce a believable number, so they are the ones worth checking for:
- Swapping part and whole. “30 is what percent of 200” gives 15%. Swap the boxes and the tool shows 666.6667%, a clue that the whole should be the bigger number.
- Adding two discounts. 20% off followed by 10% off is not 30%. Run Subtract twice: 100 becomes 80, then 72, so the real total is 28%.
- Confusing points with percent. A rate moving from 4% to 5% is one percentage point, but in Percentage change it is +25%, because the base is 4.
- Typing 0.15 in a percent box. The tool divides by 100 itself. 15 gives 37.5 of 250; 0.15 gives 0.375.
- Starting from zero or leaving a box empty. Empty fields count as 0, and a change from 0 has no percentage, so the tool shows Undefined instead of a number. With a negative start, such as −50 to −25, it divides by the absolute value and returns +50%.
Results are rounded to 4 decimal places for display, so check the formula line under the result when the sums matter.
Frequently asked questions
What is the difference between direct and inverse rule of three? ▼
In direct proportionality, when one quantity increases, the other increases at the same rate (e.g., more grams of coffee produce more cups). In inverse proportionality, an increase in one value causes a proportional decrease in the other (e.g., more workers complete the same task in fewer hours).
Why is percentage change from 100 to 150 not the same as 150 to 100? ▼
Because the base changes. Going from 100 to 150 is +50% (+50 on a base of 100). Going from 150 back to 100 is −33.33% (−50 on a base of 150).
If I add 20% and then subtract 20%, why don't I get the original number? ▼
Each operation uses a different base. Adding 20% to 100 gives 120, but subtracting 20% from 120 removes 24, leaving 96. To undo a markup you need to subtract a smaller percentage from the new total, which you can check with the Add and Subtract modes.
Why does the fraction for one third sometimes show as 3333 / 10000? ▼
In the Fractions mode the numerator and denominator you type are reduced exactly with the greatest common divisor, so 6 / 8 becomes 3 / 4 and 0.5 / 1.5 becomes 1 / 3. In the percentage and rule-of-three modes the result is first rounded to four decimal places and only then turned into a fraction, so a repeating value such as 0.3333… is shown as 3333 / 10000. Rely on the decimal and percentage figures there; the fraction in those modes is a close approximation, not an exact reduction.
How do I set up a rule of three correctly? ▼
Decide first whether the two quantities move together. Direct example: 3 kg cost 12, so 5 kg cost (12 × 5) / 3 = 20. Enter A = 3, B = 12, C = 5. Inverse example: 6 workers finish a job in 10 days, so 4 workers need (6 × 10) / 4 = 15 days. Enter A = 6, B = 10, C = 4 and choose Inverse. The most common mistake is choosing Direct for a situation where more of one thing means less of the other, which silently gives a plausible but wrong answer. Empty fields count as 0, and a division by zero is reported as undefined instead of a number.