Percentage Calculator

Every percentage problem reduces to one of three relationships between a percent (p), a part, and a whole:

1. Find the part: part = whole × (p / 100). "What is 20% of 150?" → 150 × 0.20 = 30
2. Find the percent: p = (part / whole) × 100. "30 is what percent of 150?" → (30 / 150) × 100 = 20%
3. Find the whole: whole = part / (p / 100). "30 is 20% of what?" → 30 / 0.20 = 150

Identifying which one of these you actually have is 90% of the difficulty. Once you know, the arithmetic is rote.

Polish VAT is 23%. If a receipt shows 123 zł "gross" (VAT included), the net price is NOT 123 × 0.77 = 94.71 zł. That treats 23% as a multiplier on gross instead of on net.

Gross: 123 zł
VAT: 23%
Find: net price

Correct: net = gross / (1 + VAT) = 123 / 1.23 = 100.00 zł
Wrong:   gross × (1 - VAT) = 123 × 0.77 = 94.71 zł

Difference: 5.29 zł per 100 zł of net — a 5%+ mispricing if you use the wrong formula.

A 10% increase followed by a 10% decrease does not return you to the starting value. The decrease is applied to a larger base than the original.

• Start: 100
• After +10%: 110 (= 100 × 1.10)
• After −10%: 99 (= 110 × 0.90)
• Net change: −1%, not 0%

This is why stock prices that "recovered" to break-even after a 50% drop need to gain 100% from the bottom, not 50%. The asymmetry compounds — n equal-percentage swings of opposite sign always leave you below the start.

• You are extracting net from gross on an invoice and want to avoid the "× 0.77" mistake.
• A spreadsheet column shows percentage changes and you need to confirm whether the cumulative effect compounds or adds.
• You are calculating a tip + tax + service charge and need to know whether the order of application changes the final amount (yes, sometimes — depends on whether they multiply or add to the subtotal).
• You are presenting "down 25%" vs "down 25 percentage points" and want to be sure you mean what you say.

• It will not compute compound interest with monthly contributions or annuities — use the dedicated compound interest calculator.
• It will not handle percentage point arithmetic with statistical confidence intervals — for that, use a stats tool, not a percentage calculator.
• It will not convert basis points specifically (100 bps = 1 percentage point) but you can do this manually: divide by 100.