CALTRX

Percentage Calculator

Quickly find percentages, percentage changes, and differences between values. A versatile tool for everyday math and professional calculations.

Enter your values above to see the results.

Tips & Notes

  • ✓Find 10% by moving the decimal left one place, then scale: 15% = 10% + half, 20% = double 10%.
  • ✓Undo a percentage increase by dividing, not subtracting: $125 after +25% → original = $125 ÷ 1.25 = $100.
  • ✓Percent change: always divide by the OLD value. ($96 − $80) ÷ $80 = 20%, not ÷ $96 = 16.67%.
  • ✓Convert percentages to decimals before multiplying: 7% = 0.07, so 7% of $340 = $340 × 0.07 = $23.80.
  • ✓Sequential changes multiply: +10% then +8% = 1.10 × 1.08 − 1 = 18.8% total, not 18%.

Common Mistakes

  • ✗Entering New and Old values reversed — gives wrong sign and magnitude.
  • ✗To find original before a discount: $68 after 15% off → $68 ÷ 0.85 = $80, not $68 + 15%.
  • ✗Using percent-change when percent-difference is needed — only use change when one value is a clear starting point.
  • ✗Adding sequential percentage changes: two 10% raises = 1.10 × 1.10 − 1 = 21%, not 20%.
  • ✗Reporting the decimal result without multiplying by 100: 0.25 is not 25% until you multiply by 100.

Percentage Calculator Overview

In mathematics, a percentage is a number or ratio that represents a fraction of 100, written with the symbol %. It is one of the ways to express a relationship between two numbers, alongside ratios, fractions, and decimals. For example, 35% is equivalent to the decimal 0.35 or the fraction 7/20.

The core percentage formula involves three values: the percentage P, the base value V, and the result R:

P × V = R
EX: what is 5% of 300? → 0.05 × 300 = 15
This calculator covers five common percentage problems. Each mode solves a different version of the same underlying question:
  • What is X% of Y — finds a percentage of a number. What is 15% of 200? Answer: 30.
  • X is what % of Y — finds what percentage one number is of another. 30 is what % of 200? Answer: 15%.
  • Percent change — measures how much a value increased or decreased relative to the starting value. From 80 to 100: +25%.
  • X is Y% of what — recovers the original whole when you know a part and its percentage. 30 is 15% of what? Answer: 200.
  • Add or subtract % — applies a percentage increase or decrease to a value. 200 plus 15% = 230. 200 minus 15% = 170.
Percentage increase and decrease use the same formula. The sign tells you the direction:
Change = ((New − Old) ÷ Old) × 100
EX: 500 increased by 10% → 500 × 1.1 = 550
EX: 500 decreased by 10% → 500 × 0.9 = 450
Always divide by the starting value, never the ending one. From $80 to $96: ((96 − 80) ÷ 80) × 100 = 20%. When two values have no clear starting point, use percentage difference instead:
Difference = |V₁ − V₂| ÷ ((V₁ + V₂) ÷ 2) × 100
EX: |100 − 80| ÷ ((100 + 80) ÷ 2) × 100 = 20 ÷ 90 × 100 = 22.2%
One distinction that causes widespread confusion: a percentage point and a percent change are not the same. When an interest rate rises from 4% to 6%, that is 2 percentage points (the arithmetic difference) and a 50% increase (because 2 ÷ 4 × 100 = 50%). Both statements describe the same change accurately. Compound percentage changes never simply add together. A salary rising 5% then 8% increases by (1.05 × 1.08 − 1) × 100 = 13.4%, not 13%. Select the mode that matches your question, enter what you know, and the result appears with every step shown.

Frequently Asked Questions

For 20 percent: find 10 percent first (move the decimal one place left), then double it. For 20 percent of 85: 10 percent is 8.5, doubled is 17. For 15 percent: find 10 percent and add half of that (5 percent). 15 percent of 80: 8 plus 4 = 12. For 25 percent: divide by 4. For 5 percent: find 10 percent and halve it. For any percentage that is a multiple of 5, combine these building blocks. For tip calculations specifically: on a $47 bill, 20 percent tip is easiest computed as $47 times 2 = $94, then divide by 10 = $9.40.

Divide the discounted price by (1 minus the discount rate). Example: item costs $68 after a 20% discount → original = $68 ÷ (1 − 0.20) = $68 ÷ 0.80 = $85. Verify: 20% of $85 = $17, and $85 − $17 = $68 ✓. A common mistake is subtracting the discount percentage from the final price: $68 × 0.20 = $13.60, and $68 + $13.60 = $81.60 — wrong. Always divide by (1 − rate), not multiply.

Percentage points measure absolute differences between percentages. Percent change measures the relative change. Example: interest rate rises from 2% to 3% — this is a 1 percentage point increase but a 50% increase in the rate itself. Reporting '50% increase in interest rates' is technically correct but misleading to most readers. Financial and economic reporting should always clarify which type of change is being described to avoid misinterpretation.

Because the base changes after the first operation. A 50% increase on $100 gives $150. A 50% decrease on $150 gives $75 — not $100. Mathematically: 100 × 1.50 × 0.50 = 75. The decrease is calculated on a larger base ($150), so it removes more in absolute dollars than the original increase added. To return to the original after a 50% increase, you need a 33.3% decrease (not 50%), because 150 × (1 − 1/3) = 100.

Divide the part by the whole, then multiply by 100. Formula: percentage = (part ÷ whole) × 100. Example: 45 out of 60 = (45 ÷ 60) × 100 = 75%. To find what percentage 18 is of 72: (18 ÷ 72) × 100 = 25%. Make sure you identify which number is the "part" and which is the "whole" — the whole is the total or reference value. If 30 students passed out of 40 total, the pass rate is (30 ÷ 40) × 100 = 75%. If sales increased from $200 to $250, the increase is $50, and the percentage increase is (50 ÷ 200) × 100 = 25%. Enter the values into this calculator and select the appropriate operation to get the answer with step-by-step working.

A percentage above 100% means the value exceeds the reference amount. 150% of $80 = $120 — more than the original. Growth rate of 200% means the quantity tripled (original + 200% more = 3× original). In business: revenue grew 150% means it increased by 1.5 times its original value (now 2.5× original). Percentage change above 100% is common in fast-growing companies. There is no mathematical limit — stock prices can gain 500% or 1000% over time.