Reference tables and formula sheets
Sourced tables and formula sheets that support Calxy calculators. Every page cites its sources and links to the tools that use it.
Math Formulas
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.
Math Symbols
Mathematical symbols and signs, the Greek alphabet and Roman numerals with their names, meanings and uses, linked to Calxy math calculators.
- Math SymbolsA curated list of the mathematical symbols used from arithmetic through calculus and statistics. Each entry gives the symbol's name, what it means, an example and its Unicode code point, which is derived directly from the character shown.
- Math SignsThe individual signs of arithmetic, with the exact Unicode character for each, its HTML named reference and how to enter it on common systems. Code points are derived from the characters shown.
- Greek AlphabetThe 24 letters of the Greek alphabet in order, each with its capital and small form, its Unicode code points and the quantities it usually denotes in math, statistics and science.
- Roman NumeralsRoman numerals write numbers with seven letters, I, V, X, L, C, D and M. The charts below are generated by the same converter as the Calxy Roman numeral calculator, so every entry follows the standard subtractive form.
Trigonometry
Trigonometric and inverse trigonometric functions, identities, exact values and common angle tables, linked to the Calxy trigonometry calculator.
- Trigonometric FunctionsThe three basic trigonometric functions relate an angle to ratios of lengths. This page defines them, gives exact and decimal values for every multiple of 15° from 0° to 360°, and lists the identities used most often.
- Inverse Trig ValuesThe principal values of the inverse sine, cosine and tangent at the arguments that come up most often, given exactly (as fractions of π), in decimal radians and in degrees.
- Inverse Trig Functionsarcsin, arccos and arctan undo sine, cosine and tangent on restricted intervals. This sheet gives their domains and ranges, describes their graphs and collects their derivatives, integrals and compositions with the ordinary trig functions.
Electrical
Electrical units, terms, symbols, components and circuit laws explained with formulas, linked to Calxy electrical power, energy and wiring calculators.
- Electrical UnitsThe SI units used for current, voltage, resistance, power, charge and energy, how each is built from the others, and the non-SI units such as kWh, VA and dBm that appear on bills, nameplates and datasheets.
- Electrical TermsShort, precise definitions of the quantities that appear in every circuit calculation, each with its usual symbol, SI unit and the formula that ties it to the others.
- Electrical SymbolsWhat the common schematic symbols look like and what they mean, grouped by component family. The two main conventions are IEC 60617 (used internationally) and IEEE 315 / ANSI Y32.2 (common in North America); where they differ, both drawings are described.
- Electronic ComponentsThe basic building blocks of circuits, what each one does, and the formulas used to combine them in series and in parallel.
- Electrical LawsThe laws used to analyze almost every circuit: Ohm's law for single components, Kirchhoff's laws for networks, the voltage divider rule that follows from them, and Coulomb's law for the force between charges.
Number Systems
ASCII and Unicode tables, HTML entities, Alt codes and numeral systems, linked to Calxy binary, hex and text encoding tools.
- ASCII TableAll 128 ASCII codes with their decimal, hexadecimal, binary and octal values, the printable character or control-code name, and answers to the lookups people search for most.
- Alt CodesHold Alt and type a number on the numeric keypad to enter a character on Windows. The character you get depends on whether the number starts with 0, because the two forms use different code pages.
- Unicode CharactersA curated set of frequently used Unicode characters grouped by block, each with its code point, official character name, HTML numeric reference and UTF-8 encoding. Unicode has well over 150,000 characters, so this page covers the common ones and links to the full charts.
- HTML EntitiesNamed character references and numeric codes for the characters most often needed in HTML, from the reserved characters & < > " to symbols such as ©, €, ✓ and ♥. Every name here is in the WHATWG HTML named character reference list.
- Numeral SystemsPositional number systems write the same value with different bases. This page explains place value, the digits and prefixes used for each common base, and lists 0 to 32 in binary, octal, decimal, hex and base 36.
Color
Named web colors and web-safe colors with HEX, RGB and HSL values, linked to the Calxy color converter and picker.
- Color NamesEvery named color keyword defined in CSS Color Module Level 4, with its hex code, RGB and HSL values. These names work in HTML, CSS and SVG in every modern browser.
- Web Safe ColorsThe 216-color web-safe palette with its full and shorthand hex codes, RGB values and any CSS color name that matches exactly.
Wire
AWG and SWG wire gauge tables with diameter, cross-sectional area and resistance, linked to the Calxy wire gauge and voltage drop calculators.