Percentage Calculator
The five percentage questions people actually ask, each with the working shown.
How it works
A percentage is a fraction with 100 underneath it. The arithmetic is trivial; the mistake is picking the wrong one of five questions. "What is 20% of 250,000" and "250,000 is 20% of what" are different questions with answers far apart.
The one people get wrong is the reverse question at a sale. A jacket reduced by 20% costs 240,000, so it was 240,000 ÷ 0.8 = 300,000 — not 240,000 × 1.2 = 288,000. Adding 20% back adds it to the *reduced* price, while the original 20% came off the *full* price. Different bases, different answers.
The second mistake is the denominator in a percentage change. It is always the starting value. A price going 100 → 150 has risen 50%; coming back 150 → 100 has fallen 33.3%, not 50%. The two are not symmetric because they divide by different numbers.
The working is shown under every answer so it can be checked by hand rather than taken on trust.
Formula
P% of X = X × P ÷ 100 • X as a % of Y = X ÷ Y × 100 • original = final × 100 ÷ P
All three are the same relationship between three numbers, differing only in which one is unknown. Seeing that is the quickest way to stop choosing the wrong formula.
Worked example
A jacket reduced by 20% now costs 240,000:
- The sale price as a % of the original
- 100% − 20% = 80%
- Original price
- 240,000 × 100 ÷ 80 = 300,000
- Amount saved
- 300,000 − 240,000 = 60,000
- The common wrong method
- 240,000 × 1.2 = 288,000
The wrong method is out by 12,000 on a small purchase. On a contract or a loan, the same error is out by millions.
Frequently asked questions
How do I find the price before a discount?
Divide the sale price by (100 − discount) and multiply by 100. Reduced 20% to 240,000 means the original was 240,000 ÷ 80 × 100 = 300,000.
Why does +50% then −50% not return to the start?
The two are measured against different bases. 100 rises 50% to 150; 150 falls 50% to 75. Returning to exactly 100 needs a fall of 33.3%.
Is 10% off twice the same as 20% off?
No. Two successive 10% discounts total 19%, because the second applies to the already-reduced price: 100 → 90 → 81, not 80.
What is the difference between percent and percentage points?
A rate moving from 5% to 7% has risen 2 percentage points — and 40%. The two phrasings describe the same change and leave very different impressions, which is why they are worth keeping apart.
How do I take a percentage of a percentage?
Multiply the two rates: 20% of 50% is 0.2 × 0.5 = 0.1, or 10%. This is how stacked commissions and compounding discounts work.
How does this round?
Results keep twelve significant digits to remove floating-point noise, then display up to four decimal places. The working shown is the real calculation, not the rounded one.