Math
Browse 9 professional tools
Aspect Ratio Calculator
Combinatorics & Probability Calculator
Complex Number Calculator
Equation Solver
Geometry Calculator
Graph Plotter
Matrix Calculator
Percentage Calculator
Statistics Calculator
Math tools split into "do the calculation" (statistics, equation solver, geometry) and "understand the algorithm" (matrix operations, complex numbers, combinatorics). The opinionated takes: report median + IQR for skewed data not mean + stddev; use bracketed numeric methods (Brent) for general root-finding; for matrix inversion, use LU decomposition not the closed-form adjugate formula that explodes on ill-conditioned matrices.
Calculators
Routine arithmetic and unit math. Geometry handles 30+ 2D/3D shapes with the formulas shown (Heron for triangle area from sides, etc.). Unit converter uses NIST-defined exact conversion factors (1 inch = 0.0254 m exactly, etc.).
Calculate percentages, percentage increase/decrease, find X% of Y, what percent is X of Y. Free online percentage calculator with formulas
Calculate area, perimeter, volume of 2D and 3D shapes. Circle, triangle, rectangle, sphere, cube formulas. Free online geometry calculator with diagrams
Calculate and convert image/video aspect ratios. Find dimensions for 16:9, 4:3, 21:9 and custom ratios. Free online aspect ratio calculator
Free online unit converter. Convert length (meters, feet, inches), weight (kg, lbs), temperature (Celsius, Fahrenheit), volume, area, speed and more units instantly
Convert numbers between binary, octal, decimal, hexadecimal and custom bases (2-36). Free online number system converter for programmers
Statistics & probability
Descriptive statistics with skewness/kurtosis tests (so you know whether mean+stddev is misleading). Combinatorics covers the four cases of "choose k from n" plus common probability distributions (binomial, hypergeometric, Poisson).
Calculate mean, median, mode, standard deviation, variance and more. Statistical analysis with histograms and charts. Free online statistics calculator
Calculate permutations, combinations, factorial, binomial coefficients. Probability distributions calculator. Free online combinatorics tool
Equations & algebra
Equation solver handles linear / quadratic / cubic / quartic in closed form; quintic+ via numeric methods (Newton, Brent, bisection). Matrix calculator uses LU for inverse and QR for eigenvalues — numerically stable, not the textbook formulas.
Solve linear, quadratic, cubic equations and systems of equations online. Step-by-step solutions with graphing. Free math equation solver calculator
Perform matrix operations: addition, multiplication, inverse, determinant, transpose, eigenvalues. Free online linear algebra matrix calculator
Calculate with complex numbers: addition, multiplication, division, polar form, conjugate. Visualize on Argand diagram. Free complex number calculator
Plot mathematical functions and equations. Create line, scatter, parametric graphs. Free online graphing calculator and function visualizer
Frequently asked questions
When should I report median instead of mean?
Whenever the distribution is skewed (|skewness| > 1). Income, latencies, transaction sizes, time on page — almost always skewed. Mean is pulled toward outliers; median tells the audience what the typical observation looks like. P95/P99 percentiles describe the tail.
Why does my numeric solver give different answers from different starting points?
Newton-Raphson and other iterative methods converge to whichever root the gradient leads to from your initial guess. For functions with multiple roots, the basin of attraction can be fractal. Use bisection or Brent's method on bracketed intervals if you need predictability.
Is geometric mean different from arithmetic mean?
Yes — and it matters for ratios. Geometric mean is the n-th root of the product; arithmetic mean is the sum divided by n. For multiplicative quantities (compound returns, growth rates), geometric is correct. Arithmetic mean of percentage returns over-states actual realized return.
How do I know if my matrix calculation is reliable?
Condition number κ(A). High κ means small input errors get amplified — log10(κ) is the number of decimal digits lost to roundoff. κ = 10^8 means single-precision arithmetic gives meaningless results. The matrix calculator reports condition number alongside results.
Last updated · E-Utils editorial team