Free Math Calculators
Use focused math calculators for percentages, fractions, ratios, algebra, coordinate geometry, plane geometry, trigonometry, statistics, notation, and number theory. Each page starts with the calculator, then explains the formula, result meaning, and practical use cases below the fold.
Live math calculators
Core Math
Percentage Calculator
Calculate percent of a value, part as percent of total, percent change, and increase or decrease scenarios.
Open toolCore Math
Fraction Calculator
Simplify fractions and calculate addition, subtraction, multiplication, division, decimals, and percent forms.
Open toolCore Math
Ratio Calculator
Simplify ratios, calculate shares of a total, and scale an equivalent ratio from a target quantity.
Open toolAlgebra & Coordinate Geometry
Linear Equation Solver
Solve ax + b = c equations, isolate x, and identify one-solution, identity, or no-solution cases.
Open toolAlgebra & Coordinate Geometry
Slope Calculator
Calculate slope from two points with rise, run, y-intercept, point-slope form, and vertical-line handling.
Open toolAlgebra & Coordinate Geometry
Midpoint Calculator
Find the midpoint between two coordinate points with x and y averages and ordered-pair output.
Open toolAlgebra & Coordinate Geometry
Distance Formula Calculator
Calculate straight-line distance between two coordinate points with delta x, delta y, and squared distance.
Open toolGeometry
Area Calculator
Calculate rectangle, triangle, circle, and trapezoid area with formula-backed square-unit results.
Open toolGeometry
Perimeter Calculator
Calculate square, rectangle, triangle, and circle perimeter or circumference with unit-aware formulas.
Open toolGeometry
Circle Calculator
Calculate diameter, circumference, area, sector area, and arc length from radius and angle inputs.
Open toolGeometry
Triangle Calculator
Calculate triangle perimeter, semiperimeter, Heron area, base-height area, side validity, and side type.
Open toolTrigonometry
Pythagorean Theorem Calculator
Calculate hypotenuse, missing leg, squared terms, and right-triangle checks from side inputs.
Open toolTrigonometry
Right Triangle Calculator
Calculate hypotenuse, area, perimeter, acute angles, sine, cosine, and tangent from two legs.
Open toolTrigonometry
Unit Circle Values Reference
Review common degree, radian, sine, cosine, tangent, and coordinate values for unit circle study.
Open toolStatistics
Mean Median Mode Calculator
Calculate mean, median, mode, range, sum, minimum, maximum, and sorted values from a pasted dataset.
Open toolStatistics
Standard Deviation Calculator
Calculate sample and population standard deviation, variance, mean, and squared-deviation checks.
Open toolStatistics
Percentile Calculator
Calculate percentile values with nearest-rank and interpolated methods, sorted values, and rank checks.
Open toolStatistics
Z Score Calculator
Calculate z-score, distance from mean, and approximate normal percentile from value, mean, and standard deviation.
Open toolReference
Math Formula Library
Review formulas for arithmetic, algebra, geometry, trigonometry, statistics, notation, and number theory.
Open toolNotation & Number Theory
Scientific Notation Calculator
Convert values into scientific notation, engineering notation, e notation, coefficient, and exponent form.
Open toolNotation & Number Theory
Prime Factorization Calculator
Find prime factors, exponent form, expanded factors, prime status, and positive divisor count.
Open toolNotation & Number Theory
GCD and LCM Calculator
Calculate greatest common divisor, least common multiple, and prime factor audit rows for integer lists.
Open toolCore math questions covered in this release
Percent formulas
Calculate percent of a number, percent change, part of total, and increase or decrease problems.
Fraction operations
Simplify fractions and compare addition, subtraction, multiplication, division, decimal, and percent forms.
Ratio scaling
Simplify ratios, find shares of a total, and scale equivalent ratios for recipes, maps, and classroom problems.
Algebra and lines
Solve linear equations, calculate slope, find midpoint, and measure coordinate distance from two-point inputs.
Geometry formulas
Calculate area, perimeter, circle measurements, and triangle values with unit-aware formula notes.
Statistics summaries
Calculate center, spread, percentile, and z-score values from datasets with sorted-value checks.
Notation and number theory
Convert scientific notation, factor integers, and calculate GCD or LCM from prime-factor checks.
Math tools for study, teaching, and everyday checks
Students
Check arithmetic steps while practicing homework problems without hiding the formula behind the answer.
Teachers
Create quick examples for percent, fraction, and ratio lessons with visible formulas and print-ready results.
Everyday math
Handle discounts, proportions, recipe scaling, grade calculations, and quick number comparisons.
How it works in three quick steps.
Choose the math problem type
Open the calculator that matches the question: percent, fraction, ratio, equation, coordinate, geometry, trigonometry, or statistics.
Enter the known values
Add the values from the problem statement. Each calculator keeps the assumptions visible while results update.
Read the result with the formula
Use the answer, formula explanation, and copy or print controls to support homework, teaching, or practical planning.
Reusable formula explanations across math tools
- Percent tools separate part, whole, change, and original value so the denominator is clear.
- Fraction tools reduce results and show decimal or percent forms only after the exact operation is complete.
- Coordinate tools keep deltas, averages, and squared-distance steps visible before final answers.
- Geometry and trigonometry tools pair formulas with unit notes so users do not mix linear, square, and angle units.
- Statistics tools show sorted values, sample and population spread, percentile method labels, and unitless z-scores.
- Notation and number-theory tools connect powers of ten, prime factors, GCD, and LCM to formula-library references.
Common formulas used by the math calculator library
| Family | Working formula | Quick check |
|---|---|---|
| Percent | part / whole x 100; change / original x 100 | $18 discount on $120 = 15% |
| Fractions | a/b +- c/d; a/b x c/d; (a/b) / (c/d) | 2/3 + 1/6 = 5/6 |
| Coordinate geometry | m = (y2 - y1) / (x2 - x1); M = ((x1+x2)/2, (y1+y2)/2) | points (1,2), (5,10) give slope 2 |
| Plane geometry | A = pi r^2; C = 2 pi r; A triangle = bh/2 | circle radius 3 has area 9pi |
| Trigonometry | radians = degrees x pi / 180; a^2 + b^2 = c^2 | 90 degrees = pi/2 radians |
| Statistics | mean = sum / n; s^2 = sum((x - xbar)^2) / (n - 1) | 2,4,4,6,9 has mean 5 and median 4 |
| Number theory | n = p1^a x p2^b; abs(a x b) = GCD x LCM | 360 = 2^3 x 3^2 x 5 |
External references used for formula checks
Math calculators that keep formulas visible
Toolarithm's math calculator hub begins with core arithmetic workflows that appear across homework, classroom examples, small business checks, budgeting, shopping, recipes, and quick comparisons. The current release covers percentage, fraction, ratio, linear equation, slope, midpoint, distance formula, area, perimeter, circle, and triangle calculators because those topics support many later algebra, geometry, trigonometry, and statistics tools. The hub is organized by the question a user is trying to answer: how much, what fraction, what ratio, which coordinate, what area, what angle, or what missing side.
The goal is not to hide math behind a black-box answer. The calculators show useful results quickly, but they also keep the formula and symbol definitions visible so students can connect the output to the method. Percentage pages cover percent of a value, part of total, percent change, and increase or decrease problems. Fraction tools simplify inputs and calculate common operations. Ratio tools reduce quantities, show shares, and scale equivalent relationships. Algebra tools isolate variables, describe line slope, and measure coordinate segments. Statistics tools now add mean, median, mode, standard deviation, percentile, and z-score workflows. Day 12 adds a formula library, scientific notation, prime factorization, and GCD/LCM workflows. Future math releases will expand into probability, measurement conversion, and science math while keeping the same expectation: visible variables, worked formulas, and clear limits for each result.