Online Calculators FreeReference Manual

Math Calculator

A complete math toolbox in one dropdown: GCD, LCM, primes and factorization, factorials, permutations and combinations, roots, logarithms, quadratic and linear solvers, ratios, weighted averages, list statistics, rounding and scientific notation.

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One page, every classic operation

Pick the operation from the dropdown and the form adapts: two numbers for GCD and LCM, a single field for primes and factorials, three coefficients for the quadratic solver, a comma-separated list for means and weighted averages. Every member shows the substituted formula beneath the board, so the page doubles as a worked example.

The quick reference

GCD/LCM: LCM(a, b) = |a × b| ÷ GCD(a, b). Counting: nPr = n!/(n−r)! when order matters, nCr = n!/(r!(n−r)!) when it does not. Quadratic: x = (−b ± √(b² − 4ac)) ÷ 2a — a negative discriminant means no real roots. Logs: logₑ(x) = ln x ÷ ln b for any base. Weighted average = Σwx ÷ Σw.

Worked example

  1. Solve x² − 5x + 6 = 0 with the Quadratic member.
  2. a = 1, b = −5, c = 6, so the discriminant is 25 − 24 = 1.
  3. x = (5 ± 1) ÷ 2, giving x₁ = 3 and x₂ = 2.
  4. The board also lists the discriminant and the vertex (2.5, −0.25).

How to use it

  1. Choose the operation from the dropdown.
  2. Fill the fields that appear — lists go in as comma-separated numbers.
  3. Read the result, the extra rows, and the substituted formula.
  4. Copy, print, or share the link — it remembers the member and your values.

Frequently asked questions

How do I find the LCM of three numbers?

Leave the optional third field filled: LCM(a, b, c) = LCM(LCM(a, b), c). The tool does exactly that and shows the GCD of the same inputs as a bonus row.

What is the difference between a permutation and a combination?

Order. nPr counts ordered selections — a gold-silver-bronze podium — while nCr counts unordered ones, like a hand of cards. P(10, 3) = 720 but C(10, 3) = 120.

Is 1 a prime number?

No. A prime has exactly two distinct divisors, 1 and itself; 1 has only one divisor. The prime checker explains this for any input below 2.

Why does my quadratic equation fail?

The solver only returns real roots. If the discriminant b² − 4ac is negative the two roots are complex, and the tool tells you the discriminant so you can see why. Setting a = 0 is also rejected because the equation is then linear.

How do significant figures differ from decimal places?

Decimal places count digits after the point (3.14159 → 3.142 to 3 decimals); significant figures count from the first non-zero digit (3.14159 → 3.14 to 3 sig figs, 0.00567 → 0.0057). The rounding member shows both at once.

How does the decimal-to-fraction converter work?

It searches every denominator from 1 to 10,000 and keeps the fraction with the smallest error, so 0.375 lands exactly on 3/8 while 0.14159 gets the closest match such as 33/233.