Math Calculators

Calculate what X% of a value is, find what percentage one number is of another, or compute the percentage change between two numbers.

Convert any fraction n/d to its decimal form, including detection of repeating decimals.

Convert a terminating decimal to its simplified fraction form.

Simplify a ratio like 12:18 to its lowest terms (2:3) and compare to a target ratio.

Given a/b = c/x (or any of three knowns), solve for the fourth.

Compute the arithmetic mean of a list of numbers.

Find the middle value (or average of two middle values) of a list of numbers.

Find the most frequently occurring value (or values) in a list.

Compute the range (max − min) of a list of numbers.

log_b(x) for any base b > 0, b ≠ 1, x > 0. Common bases shown side-by-side.

b^x — the inverse of a logarithm. Given the log value and base, recover the original number.

A = A₀ · e^(kt) for continuous growth, or A = A₀ · (1 + r)^t for discrete.

A = A₀ · e^(-kt). Compute remaining quantity, half-life, or decay constant.

A = P · e^(rt) — the limit of compound interest as the compounding frequency → ∞.

Euclidean algorithm: gcd(a,b) = gcd(b, a mod b). Supports 2-6 integers.

lcm(a,b) = |a × b| / gcd(a,b). Smallest number that both a and b divide evenly.

Is n prime? Trial division up to √n; identifies smallest divisor and nearest primes if composite.

n = p₁^a₁ × p₂^a₂ × … Trial division to find all prime factors with multiplicity.

n! = 1 × 2 × … × n. Computes exactly up to 21! (number limit); approximate via Stirling for larger.

Convert decimal ↔ scientific notation. Standard form a × 10^b with 1 ≤ |a| < 10.

√n with integer-perfect-square check, simplified surd form, and decimal expansion.

∛n with perfect-cube detection, simplified surd form, and decimal expansion.

ⁿ√x = x^(1/n). Generalizes square and cube roots to any positive integer n.

b^x — supports fractional, negative, and zero exponents.

ax² + bx + c = 0 → roots via discriminant. Real or complex.

ax + b = 0 → x = −b / a. Single-variable linear equations in standard form.

Solve a₁x + b₁y = c₁; a₂x + b₂y = c₂. Cramer's rule via determinants.

Evaluate polynomial p(x) = aₙxⁿ + … + a₁x + a₀ at any x. Up to degree 6.

Convert any integer between binary (2), octal (8), decimal (10), and hexadecimal (16).

a mod n: remainder of a divided by n. Always non-negative for positive n.

(a + bi) ± (c + di), ×, ÷. Real part, imaginary part, modulus, argument.

Operations vs. n for common Big-O classes: O(1), O(log n), O(n), O(n log n), O(n²), O(2ⁿ).

aₙ = a₁ + (n−1)d. Find any term of an arithmetic sequence.

aₙ = a₁ × r^(n−1). Find any term of a geometric sequence.

Sₙ = n × (a₁ + aₙ) / 2 = n/2 × (2a₁ + (n−1)d).

Sₙ = a₁(1 − rⁿ) / (1 − r) for r ≠ 1. Infinite: S∞ = a₁/(1−r) if |r|<1.

F(n) = F(n−1) + F(n−2). 0, 1, 1, 2, 3, 5, 8, 13, 21, ...

H = n / Σ(1/xᵢ). Used for averaging rates and ratios.

WA = Σ(value × weight) / Σ(weight). Generalizes the arithmetic mean.

d/dx(aₙxⁿ + … + a₁x + a₀) = naₙxⁿ⁻¹ + … + a₁. Power rule.

∫ₐᵇ p(x) dx using power rule for antiderivatives.

lim x→a of polynomial ratios (basic substitution + L'Hopital for 0/0).

Approximate sin/cos/eˣ/ln(1+x) via Taylor polynomial of degree n.

xₙ₊₁ = xₙ − f(xₙ) / f'(xₙ). Iteratively find roots of polynomial.

Approximate ∫ₐᵇ f(x) dx using N rectangles (left, right, midpoint).

P(x) / [(x−a)(x−b)] = A/(x−a) + B/(x−b). Distinct linear factors only.

a+b · a−b · a·b (dot, scalar) · a×b (cross, vector perpendicular to both) · |a|, |b|, angle.

det = a(ei−fh) − b(di−fg) + c(dh−eg). Cofactor expansion.

Roots of λ² − tr(M)λ + det(M) = 0.

Base × height, Heron's formula (SSS), or side-angle-side (SAS) — pick the inputs you have.

All four classic circle quantities in one tool — area πr², circumference 2πr, sector area (½r²θ), arc length (rθ).

Solve { a·x + b·y = e ; c·x + d·y = f } via Cramer's rule. Handles unique / no-solution / infinite-solutions cases.

Determinant and inverse for 2×2 or 3×3 matrices. Inverse exists iff det ≠ 0.

Basic event probabilities + union + intersection + conditional + Bayes' theorem from two-event inputs.

All 5 descriptive statistics from a list of numbers — sample + population variants for std dev / variance.

Convert (x, y) ↔ (r, θ). Polar: r = √(x²+y²), θ = atan2(y, x). Cartesian: x = r·cos θ, y = r·sin θ.

Closed-form roots for linear, quadratic, cubic (Cardano), and quartic (Ferrari) polynomials. Complex roots supported.

Solve a·log_base(x) + c = target, a·base^x + c = target, or A·e^(kx) = target — pick the equation form.

Recognizes the 30 most-used trigonometric identities and shows the simplified form. Pattern-library based — not a general symbolic algebra system.

Convert between Roman numerals and Arabic integers (1–3999). Strict subtractive-form validation — flags malformed numerals like IIII or VC.