Math
Percentage Calculator
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How to use it
Using the percentage calculator
- 01
Pick your question type
Percent of a number, share of a total, or growth between two values.
- 02
Fill both values
The labels stay generic (first/second) because their meaning changes per mode; the help text explains each role.
- 03
Read the single clear answer
One headline result plus supporting rows like ratio and remainder.
Good to know
One tool, three confusions
Most percentage mistakes come from mixing up the question: “20% off” versus “20% more”, or “what percent of my income” versus “how much did it grow”. Choosing the mode first forces clarity about which number is the base, and the base is everything.
The base rule
Whatever follows the word “of” is the base. 30% of 40 and 40% of 30 land on the same 12, but 30 as a percent of 40 is a completely different 75%. When results look absurd, re-check which value sat where.
Change needs a starting point
Percentage change divides by where you started, so going 50 → 75 is +50% while 75 → 50 is −33.3%. The asymmetry is real mathematics, not an error; percentages do not round-trip.
How it's calculated
The math behind this calculator
X% of Y = Y × X/100
X is what % of Y = X/Y × 100
% change = (Y − X)/X × 100All three questions reduce to one multiplication or division once you identify which number is the base. The mode selector fixes the roles so the same two inputs answer whichever question you are actually asking, and the help line under each field restates its meaning for the chosen mode.
Assumptions & limitations
- Percent-of mode treats the second value as the base.
- Change mode is undefined from zero and reports that explicitly.
- Results render with up to six decimal places before rounding kicks in.
Worked example
15% of 80 is 12; the calculator multiplies 80 by 0.15.
FAQ
Frequently asked questions
- Which number goes first?
- In “X% of Y” the percent comes first. In “is what % of” the part comes first and the whole second. In change mode they are start then end.
- Why does change from zero fail?
- Division by zero has no defined percentage; every positive endpoint would be “infinite” growth. Use absolute difference instead.
- Can I use negative numbers?
- Yes for all modes; signs carry through, though interpreting a negative base deserves extra care.
- How precise are the results?
- Up to six decimals are shown before formatting rounds, enough for finance-grade comparisons at everyday magnitudes.
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