Math Formula Reference

Sourced math formula sheets and tables for algebra, geometry, statistics, exponents, logarithms and number facts, linked to the calculators that use them.

• Plane Geometry FormulasArea and perimeter formulas for the common flat (two-dimensional) shapes. The area formulas are the same ones the Calxy area calculator evaluates, so you can check any result against the sheet.
• Solid Geometry FormulasVolume and surface area formulas for three-dimensional solids. These are the exact formulas the Calxy volume calculator uses, listed with the measurements each one needs.
• Statistics FormulasThe core descriptive statistics formulas in one place, with the notation explained and a worked example computed by the same engine as the Calxy statistics calculator.
• Algebra FormulasThe algebra formulas used most often in school and in practice: the quadratic formula, the special products and factoring patterns, and the equations of straight lines.
• Factorial TableThe factorial n! is the product of all whole numbers from 1 to n. The table gives every factorial from 0! to 30! exactly, computed with arbitrary-precision integers rather than rounded floating-point numbers.
• Logarithm RulesA logarithm answers the question “to what power must the base be raised to get this number?” This sheet collects the log and ln rules, special values, calculus formulas and a computed table of common values.
• ConvolutionConvolution combines two functions by sliding one across the other and summing (or integrating) their products. It appears in signal processing, probability and polynomial multiplication.
• Addition TableA 12 × 12 addition chart. Find the first number in the left column and the second along the top; the cell where they meet is the sum.
• Euler's Number ee is the base of the natural logarithm and of continuous growth. It is irrational (and transcendental), so its decimals never end or repeat. Below it is defined, calculated and shown to 50 decimal places.
• Exponent RulesExponents say how many times a base is multiplied by itself: aⁿ = a × a × … × a (n factors). These rules let you multiply, divide and simplify powers without expanding them.
• Fibonacci SequenceEach Fibonacci number is the sum of the two before it, starting from 0 and 1: 0, 1, 1, 2, 3, 5, 8, 13, … The table lists F(0) through F(50) exactly, computed by the same engine as the Calxy Fibonacci calculator.
• Multiplication TableTwo multiplication charts: the 10 × 10 table of basic facts and the 12 × 12 table taught in many schools. Find one factor in the left column and the other in the top row; the product is where they meet.
• Percent, Per Mille and PPMPercent, per mille and parts-per notation are all ways of writing a dimensionless ratio as a multiple of a power of ten. This sheet defines each one and shows how to convert between them.
• Prime NumbersA prime number is a whole number greater than 1 whose only positive divisors are 1 and itself. The first 200 primes are listed below, generated by the same primality test the Calxy prime factorization calculator uses.
• Probability FormulasThe rules of probability, the key counting formulas and the two distributions used most, the binomial and the normal, with a standard normal table computed by the Calxy statistics engine.