Percentage Calculator — seven everyday percentage questions, answered as you type
Percentage Calculator
Every percentage question people actually ask is one of seven shapes. Each card below
is one shape — type your numbers and the answer appears instantly, with the working
shown so you can check it by hand. Covers tips, sales tax, discounts, markups, exam
scores, price changes and the percentage-points trap. For ratios and proportions see the
Ratio Calculator; for fractions and scientific math the
Scientific Calculator.
1. What is P% of X?
% of
=
15% of 200 → 0.15 × 200 = 30 (a 15% tip on a 200 bill).
2. X is what percent of Y?
is what percent of
=
30 out of 200 → 30 ÷ 200 × 100 = 15% (30 correct answers on a 200-question sheet).
3. Percent change: from X to Y
from
to
=
80 → 100 is a 25% increase, but 100 → 80 is only a 20% decrease — the base matters.
4. Increase or decrease X by P%
%
=
250 + 12% = 280 (price plus tax); flip the selector for a 20% discount.
5. Reverse: the final price is Z — what was the original?
final value
after
%
→ original =
280 after +12% tax → 280 ÷ 1.12 = 250. Do NOT subtract 12% from 280 — that gives 246.4, which is wrong.
6. Margin & markup from cost and price
cost
price
→ margin = of the price,
markup = over the cost
Same 10 profit: it is 25% of the cost (markup) but only 20% of the price (margin). Markdowns, tax and fees are always taken against the starting number.
7. Percentage points vs relative percent
from %
to %
=
30% → 35% is +5 percentage points, but a +16.67% relative change. News headlines mix these up constantly.
Try an example:
The one formula behind cards 1–5: a percentage is just a fraction with
a denominator of 100 — P% = P/100. Every result above is some arrangement of
part ÷ whole or whole × P/100.
Privacy: all arithmetic happens in this tab; nothing is uploaded.
What is a percentage, really?
"Per cent" literally means per hundred. 15% is the fraction 15/100 = 0.15 wearing
a costume. That is why every percentage question reduces to one of two moves:
multiply when you have the whole and want the part (15% of 200 = 200 × 0.15 = 30),
and divide when you have the part and want the share (30 out of 200 = 30 ÷ 200 = 0.15 = 15%).
Question shape
Move
Example
P% of X
X × P/100
15% of 200 = 30
X is what % of Y
X ÷ Y × 100
30 of 200 = 15%
change X → Y
(Y − X) ÷ X × 100
80 → 100 = +25%
X ± P%
X × (1 ± P/100)
250 + 12% = 280
reverse from Z
Z ÷ (1 ± P/100)
280 ÷ 1.12 = 250
The three mistakes everybody makes
1. Percent changes don't add. A 10% raise followed by another 10% raise is
not 20% — it is 1.10 × 1.10 = 1.21, a 21% raise, because the second raise
applies to the already-raised salary. Going up 25% and back down 25% leaves you at
0.75 × 1.25 = 93.75% of where you started.
2. The base changes direction. 80 → 100 is +25% (base 80), but
100 → 80 is −20% (base 100). A "25% off then 25% restocking fee" loses money
for the same reason.
3. Percentage points ≠ percent. An approval rating moving from 30% to 33%
rose 3 points but 10 percent relative to itself. Card 7 keeps the two apart.
Margin vs markup once and for all
Both describe the same profit, but against a different base: markup is profit
over cost, margin is profit over price. A 2× price over cost
(cost 50, price 100) is a 100% markup but only a 50% margin. Since price is always bigger
than cost, margin is always the smaller percentage — mixing them up overstates profit.
Cost
Price
Profit
Markup
Margin
40
50
10
25%
20%
50
100
50
100%
50%
25
100
75
300%
75%
FAQ
Why is my reverse-percentage answer "wrong"? — because subtracting the percent
from the final number uses the wrong base; always divide by (1 ± P/100) instead. Can a percent change exceed 100%? — yes: 40 → 100 is a +150% change; it just
means the new value is 2.5× the old one. What about percent difference (no direction)? — when neither value is the
"before", divide by the average of the two: |A−B| ÷ ((A+B)/2) × 100. Does it round? — display only, and only trailing noise is trimmed; the arithmetic
itself uses full precision, so chains like card 4 → card 5 stay exact. Is my data sent anywhere? — no: no server, no storage, no analytics; the page
runs locally.
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