Topical hub
Free Math Calculators
Algebra, geometry, statistics, probability and number tools with formulas shown.
85 calculators across 5 semantic clusters — free forever, instant results, downloadable PDF reports.
- Always Free
- No Hidden Costs
- No Account Required
- Unlimited Calculations
- Instant Reports
Mathematics calculators are only useful when the working is visible. Every tool in this hub states the formula it applies, defines each variable, and shows a worked example so the result can be checked by hand rather than trusted blindly.
The hub follows the standard curriculum structure. Algebra covers equations, exponents, roots and sequences. Geometry covers plane figures, solids, triangles and coordinate work. Statistics and probability cover distributions, dispersion, inference and counting. Number tools cover bases, factors, rounding and notation.
These areas overlap deliberately. The Pythagorean theorem is a geometry result used inside distance and hypotenuse calculations; combinations and permutations from counting theory feed binomial probability; standard deviation feeds z-scores, confidence intervals and sample-size planning.
Academic grade tools sit alongside them because they are weighted-average problems in disguise. GPA, CGPA, class rank and test-score calculators all apply the same weighted mean, only with credit hours or point scales as weights.
Work through a cluster rather than a single tool when you are learning: solve the equation, then verify it graphically with slope and midpoint, then check the statistical significance of a result with the inference tools.
Calculator directory
Algebra & Equations
Solving for unknowns and manipulating expressions.
Free Percentage Calculator
Percent of a number, percent change, and reverse percent problems.
Free Percent Error Calculator
Absolute and percent error between a measured and accepted value.
Free Fraction Calculator
Add, subtract, multiply, or divide two fractions with simplification.
Free Exponent Calculator
Compute any base raised to any power, including fractional and negative.
Free Log Calculator
Logarithm in any base, plus natural log and log base 10.
Free Root Calculator
nth root of a number.
Free Quadratic Formula Calculator
Solve ax² + bx + c = 0 for real or complex roots.
Free Ratio Calculator
Solve A:B = C:D for the missing term.
Free Percentage Change Calculator
Increase or decrease between two numbers.
Free Factorial Calculator
n! for whole numbers, with digit count.
Free Sequence Calculator
Arithmetic and geometric sequence terms and sums.
Free Complex Number Arithmetic Calculator
Add, subtract, multiply and divide complex numbers.
Free Cubic Equation Root Calculator
Real root(s) of ax³ + bx² + cx + d = 0.
Free Linear Equation Solver
Solve ax + b = c for x.
Free Parallelogram Area Calculator
Area of a parallelogram from base and height.
Free System of Two Equations Calculator
Solve a1x + b1y = c1 and a2x + b2y = c2.
Free Modulo Calculator
Remainder of a division (a mod n).
Free Proportion Solver
Solve for the missing value in a/b = c/d.
Geometry & Shapes
Length, area, volume and angle in two and three dimensions.
Free Slope Calculator
Slope and equation of a line from two points.
Free Distance Formula Calculator
Euclidean distance between two 2D or 3D points.
Free Circle Calculator
Area, circumference, and diameter from a circle radius.
Free Triangle Calculator
Area, perimeter, and heights from three sides (Heron's formula).
Free Right Triangle Calculator
Hypotenuse and angles from the two legs.
Free Pythagorean Theorem Calculator
Find the missing side of a right triangle: a² + b² = c².
Free Box Surface Area Calculator
Surface area and volume of a rectangular box.
Free Cone Calculator
Volume and surface area of a right circular cone.
Free Coordinate Reflection & Rotation Calculator
Reflect or rotate a 2D point.
Free 3D Cross Product Calculator
Cross product and magnitude of two 3D vectors.
Free Cube Calculator
Volume, surface area and diagonal of a cube.
Free Cylinder Calculator
Volume and surface area of a cylinder.
Free Dot Product Calculator
Dot product and angle between two 2D vectors.
Free Ellipse Calculator
Area and approximate perimeter of an ellipse.
Free Hypotenuse Length Calculator
Find the hypotenuse of a right triangle.
Free Law of Cosines Calculator
Find a side from two sides and the included angle.
Free Law of Sines Calculator
Find a missing side or angle using the law of sines.
Free Midpoint Calculator
Midpoint between two coordinate points.
Free Polygon Angles Calculator
Interior and exterior angles of a regular polygon.
Free Pyramid Volume Calculator
Volume of a pyramid with a square base.
Free Rectangle Area Calculator
Area and perimeter of a rectangle.
Free Regular Polygon Area Calculator
Area and perimeter of a regular polygon.
Free Sector & Arc Length Calculator
Arc length and sector area from radius and angle.
Free Similar Triangles Scale Calculator
Scale factor and missing side of similar triangles.
Free Sphere Calculator
Volume and surface area of a sphere.
Free Trapezoid Area Calculator
Area of a trapezoid from parallel sides and height.
Free Vector Addition & Magnitude Calculator
Add two 2D vectors and find the resultant magnitude.
Statistics & Probability
Describing data and quantifying uncertainty.
Free Statistics Calculator
Mean, median, mode, range, variance, and standard deviation.
Free Probability Calculator
P(A ∪ B), P(A ∩ B), and conditional probability from two events.
Free Permutation and Combination Calculator
Count ordered permutations P(n,r) and unordered combinations C(n,r).
Free Random Number Generator
Uniformly random integers or decimals in any range.
Free Average Calculator
Mean of a list of numbers, plus sum and count.
Free Combination Calculator
nCr combinations and nPr permutations.
Free Binomial Probability Calculator
Probability of exactly k successes in n trials.
Free Coin Flip Probability Calculator
Chance of getting exactly k heads in n flips.
Free Confidence Interval Calculator
Confidence interval for a sample mean.
Free Correlation Coefficient Calculator
Pearson's r between two paired data sets.
Free Dice Probability Calculator
Odds of a target sum when rolling multiple dice.
Free Expected Value Calculator
Average outcome of a probabilistic bet or event, over the long run.
Free Linear Regression Calculator
Best-fit line (y = mx + b) through paired data.
Free Margin of Error Calculator
Margin of error for a survey proportion.
Free Mean, Median & Mode Calculator
Central tendency of a data set: mean, median and mode.
Free Normal Distribution Probability Calculator
Probability that X falls below, above or between values.
Free Percentile Calculator
Find the percentile rank of a value in a data set.
Free Poisson Distribution Calculator
Probability of k events given an average rate λ.
Free Quartiles & IQR Calculator
Q1, median, Q3 and interquartile range with outlier bounds.
Free Sample Size Calculator
Minimum sample size needed for a survey.
Free Standard Deviation Calculator
Sample and population standard deviation and variance.
Free Variance Calculator
Sample and population variance of a data set.
Free Weighted Average Calculator
Average of values weighted by importance.
Free Z-Score Calculator
How many standard deviations a value is from the mean.
Number Tools & Notation
Bases, factors, rounding and precision.
Free GCF and LCM Calculator
Greatest common factor and least common multiple of two integers.
Free Prime Number Calculator
Check primality and list all prime factors.
Free Half-Life Calculator
Amount remaining after time for exponential decay.
Free Scientific Notation Calculator
Convert a number to and from scientific notation.
Free Matrix Calculator (2×2)
Determinant and inverse of a 2×2 matrix.
Free Rounding Calculator
Round to decimal places, integer, tens, hundreds, thousands.
Free Significant Figures Calculator
Round a number to a chosen number of sig figs.
Free Divisors & LCM Chain Calculator
All divisors, GCD and LCM across up to four numbers.
Academic & Grades
Weighted averages applied to education.
Free GPA Calculator
Weighted grade-point average from letter grades and credit hours.
Free CGPA Calculator
Cumulative GPA across multiple semesters, weighted by credits.
Free High School GPA Calculator
Weighted high school GPA with Regular, Honors, and AP/IB boosts.
Free GPA to Percentage Calculator
Convert a 4.0-scale GPA (or 10-scale CGPA) into a percentage.
Free Percentage to GPA Calculator
Convert a percentage grade into a 4.0-scale GPA or 10-point CGPA.
Free Grade Calculator
Final exam score needed to reach a target course grade.
Free Test Score Calculator
Convert correct answers into percentage, letter grade, and curved score.
Free Class Rank Percentile Calculator
Convert a class rank into a top-N% percentile.
Key concepts in math calculators
- Variable
- A symbol standing for an unknown or changing quantity in an expression or equation.
- Coefficient
- The numeric multiplier attached to a variable term, such as the 3 in 3x².
- Discriminant
- b² − 4ac in a quadratic; its sign tells you whether roots are real, repeated or complex.
- Slope
- Rate of change between two points, (y₂ − y₁)/(x₂ − x₁).
- Standard deviation
- The typical distance of observations from the mean, the square root of variance.
- Z-score
- How many standard deviations an observation sits from the mean, enabling comparison across scales.
- Probability
- Favourable outcomes divided by total outcomes, bounded between 0 and 1.
- Permutation
- An ordered arrangement of items, nPr = n!/(n−r)!.
- Combination
- An unordered selection of items, nCr = n!/(r!(n−r)!).
- Weighted average
- The sum of value × weight divided by the sum of weights — the engine behind GPA and grade tools.
How this topic works
Solving equations systematically
Linear equations isolate the unknown by applying inverse operations to both sides. Quadratics use the formula x = (−b ± √(b² − 4ac)) / 2a, where the discriminant determines the nature of the roots. Systems of two equations resolve by substitution or elimination — elimination is faster when coefficients align, substitution when one variable is already isolated. Every solution should be substituted back into the original equation as a check.
Geometry: plane figures and solids
Plane geometry works from perimeter and area formulas: rectangle A = lw, triangle A = ½bh, circle A = πr², trapezoid A = ½(a+b)h. Solids extend these into volume and surface area: cylinder V = πr²h, cone V = ⅓πr²h, sphere V = 4/3πr³. Triangle work relies on the Pythagorean theorem for right triangles and the laws of sines and cosines for oblique ones.
Descriptive versus inferential statistics
Descriptive statistics summarise the data you have — mean, median, mode, variance, standard deviation, quartiles and IQR. Inferential statistics generalise to a population you have not fully observed, using confidence intervals, margins of error, sample-size planning and regression. Confusing the two produces overconfident conclusions from small samples, which is why margin-of-error and sample-size tools belong beside the descriptive ones.
Counting before probability
Most probability errors are counting errors. Decide first whether order matters: if it does, use permutations; if it does not, use combinations. Then check whether selections are made with or without replacement. Only once the sample space is counted correctly do binomial, Poisson and dice or coin probability formulas produce meaningful answers.
Number systems and precision
Base conversion (binary, octal, decimal, hexadecimal) underpins computing; scientific notation and significant figures govern precision in science and engineering. Rounding rules matter: round-half-up and round-half-even give different long-run totals, and carrying too many significant figures implies precision the measurement never had.
Frequently asked questions
What is the difference between permutations and combinations?
Permutations count ordered arrangements, combinations count unordered selections. Choosing three ranked finishers from ten runners is a permutation; choosing a committee of three is a combination.
When should I use median instead of mean?
Use the median when the distribution is skewed or contains outliers — income, house prices, response times. The mean is appropriate for roughly symmetric data and is required for further parametric analysis.
What does the discriminant tell me?
In ax² + bx + c, if b² − 4ac is positive there are two distinct real roots, if zero there is one repeated root, and if negative the roots are a complex conjugate pair.
How do I know if my sample size is large enough?
Sample size depends on the confidence level, acceptable margin of error and expected variability. The sample size calculator inverts the margin-of-error formula so you can specify the precision you need first.
Are GPA calculations mathematics tools?
Yes — GPA, CGPA and weighted grade calculations are all weighted averages where credit hours act as weights, which is why they sit in this hub.
How many significant figures should I keep?
Match the least precise measurement in the calculation. Reporting more digits than your inputs justify implies precision that does not exist.
Do these calculators show the working?
Each page states the formula, defines every variable and includes worked examples so you can reproduce the result by hand.
Other calculator hubs
Free Finance Calculators
Loans, mortgages, investing, tax and business maths in one connected hub.
Free Health & Fitness Calculators
Body composition, nutrition, training load and clinical ratios, semantically linked.
Free Date & Time Calculators
Durations, business days, countdowns and time-unit arithmetic.
Free Construction & Home Improvement Calculators
Material quantities, coverage and waste factors for building projects.
Free Unit Conversion Calculators
Length, area, volume, weight, temperature, energy, pressure, speed and data units.
Free Everyday & Utility Calculators
Vehicles, energy bills, weather, shopping and other practical tools.