Pick the question.
Four tabs, four questions: FIND (what is X% of Y), IS (X is what % of Y), CHANGE (percent change from X to Y) and ADJUST (X ± Y%). The sentence at the top rewrites itself to match.
TAB → SENTENCE
01
The instrument.
Pick a question, fill the blanks — the sentence is the interface. The answer solves live on every keystroke, and beneath the screen the complete written proof assembles itself: percent to fraction, the arithmetic, any cancellation, and the check that runs the result backwards.
What is
%
of
?
is what percent of
?
Percent change from
to
?
%
TRY
THE WORK — STEP BY STEP
LIVE
SWS-PC/01·4 QUESTION MODES·EXACT RATIONAL CORE·0 TRACKING
02
How to use it.
Ninety seconds to full fluency — the interface is a sentence. If you can ask the question, you can already use the tool.
Fill the blanks.
Type straight into the sentence — decimals and negative numbers included. The slots grow and shrink to fit exactly what you type.
15 · 200 → 15% OF 200
No equals needed.
The screen solves live on every keystroke. The big line is the answer; the sentence above echoes exactly what you asked, so you can always see the question and its result together.
15% OF 200 → 30
Read it every way.
Below the answer: the fraction or decimal form, the multiplier where it applies, and a CHECK row that proves the result by running it backwards.
CHECK: 30 ÷ 200 = 15% ✓
Follow the work.
THE WORK panel writes the method the way a margin would — percent to fraction, the multiplication, any cancellation, and the check. Switch tabs freely; each question remembers its own numbers.
15% = 3/20 × 200 = 30
Steal the shortcuts.
The field notes pin the mental-math tricks: 10% is one decimal-slide left, 5% is half of that, 25% is half of a half, 50% is just half. Compute in your head; verify here.
10% OF 63 = 6.3
studywithstem:worked-example
ONE CALCULATION
15% of 200
├── percent15/100 = 3/20
├── ofmultiply: 3/20 × 200
├── cancel200 ÷ 20 = 10
├── multiply3 × 10 = 30
└── check30 ÷ 200 = 15%
RESULT 30 · EXACT · CHECKED BOTH WAYS
03
Frequently asked.
The questions that keep coming back about percentages — answered once, in full.
Q1 How do I calculate a percentage of a number?
Turn the percent into a decimal (divide it by 100) and multiply. For 15% of 200: 15 ÷ 100 = 0.15, then 0.15 × 200 = 30. The FIND tab does exactly this and shows every line.
Q2 How do I calculate what percent one number is of another?
Part over whole, times 100. For 30 is what percent of 200: 30 ÷ 200 = 0.15, and 0.15 × 100 = 15%. The IS tab writes these steps live.
Q3 How do I calculate percentage increase or decrease?
Change divided by the original, times 100. From 40 to 50: the change is +10, the original is 40, so 10 ÷ 40 × 100 = 25% — a 25% increase. A negative result means a decrease. The CHANGE tab measures and checks both.
Q4 How do I add or subtract a percentage from a number?
Find the percentage of the number, then add or subtract it: 200 + 15% means 15% of 200 = 30, then 200 + 30 = 230. Shortcut: multiply by 1.15 (or 0.85 for minus). The ADJUST tab shows both routes, every time.
Q5 Why does percent change divide by the original value?
Because percent means "per hundred of something" — and that something is where you started. The same distance gives different percentages from different starting points: 40 → 50 is a 25% increase, but 50 → 40 is only a 20% decrease. Same 10, different base.
Q6 What is the difference between percent change and percent difference?
Percent change is directional — it measures the new value against the old one, so order matters. Percent difference is symmetric — it measures two values against their average, and is used when neither is "the original", such as comparing two experimental results. This tool computes percent change.
Q7 What does the line over some decimals mean?
It marks a repeating decimal: 33.3 with a bar over the final 3 means 33.333…%, forever, with no rounding. Results like 1 ÷ 3 never terminate, so the calculator shows the exact repeating block instead of pretending it's 33.33.
Q8 Is it free, and does my input leave the page?
Completely free — no sign-up, no locked features. All arithmetic runs locally in your browser; nothing is recorded or transmitted, and the page keeps working offline once it has loaded.