HomeCategoriesMathematics, Statistics & Geometry

Mathematics, Statistics & Geometry Calculators

127 Total Calculators

Solve algebra, geometry, statistics, calculus, fractions, ratios, and scientific notation problems with step-by-step math calculators.

Vectors & Matrices

(3)

Angle Between Vectors Calculator

Find the angle between two 2D or 3D vectors. Shows step-by-step vector dot products, magnitudes, and conversion formulas.

Cross Product Calculator

Calculate the cross product of two 3D vectors instantly. Find the resulting perpendicular vector and its magnitude with a clear, step-by-step mathematical breakdown.

Dot Product Calculator

Use this free vector dot calculator to compute the dot product of 2D or 3D vectors. Find the scalar product and angles with step-by-step vector formulas.

Statistics & Probability

(27)

ANOVA Calculator

Perform a one-way ANOVA test for three groups. Calculate the F-statistic, p-value, sum of squares, and mean squares to compare group means.

Bayes Theorem Calculator

Calculate posterior probability using Bayes Theorem. Find P(A|B) given prior probabilities and conditional likelihoods with clear steps.

Binomial Distribution Calculator

Calculate exact binomial probabilities, cumulative distributions, mean, and variance. See full step-by-step formulas for statistics homework.

Chi-Square Distribution Probability Calculator

Calculate the p-value and cumulative probability for the Chi-Square distribution. Uses Wilson-Hilferty normalization for high precision.

Chi-Square Test Calculator

Perform a Chi-Square Goodness-of-Fit test instantly. Compare observed and expected frequencies to calculate χ², degrees of freedom, and p-value.

Conditional Probability Calculator

Calculate the probability of an event given that another event has occurred. Find P(A|B) instantly using the conditional probability formula.

Confidence Interval Calculator

Calculate the confidence interval for a sample mean. Find the margin of error and upper/lower bounds at your chosen confidence level instantly.

Expected Value Calculator

Calculate the expected value E(X) and variance of a discrete probability distribution. Essential for risk analysis and statistical modeling.

Exponential Distribution Calculator

Calculate the probability density (PDF) and cumulative probability (CDF) for continuous exponential decay and wait-time distributions.

F-Distribution Probability Calculator

Evaluate the precise p-value of an F-statistic using the Wilson-Hilferty transformation. Essential for ANOVA and variance comparison tests.

Interquartile Range Calculator

Calculate Q1, Q3, and the Interquartile Range (IQR) from a dataset. Automatically flags mathematical outliers using the 1.5 IQR rule.

Linear Regression Calculator

Perform OLS regression on any dataset. Calculate the slope, intercept, R-squared, and Pearson correlation coefficient with a clear breakdown.

Logistic Regression Calculator

Perform binary logistic regression using gradient descent optimization to model probability curves and find decision boundaries.

Margin of Error Calculator

Determine the statistical margin of error for survey proportions using precise Z-scores for 90%, 95%, and 99% confidence intervals.

Mean Absolute Deviation Calculator

Calculate the MAD for any dataset to understand dispersion. Provides a robust alternative to standard deviation that ignores extreme outliers.

Multiple Regression Calculator

Perform advanced multivariate OLS regression. Calculates exactly how two independent variables (X₁, X₂) jointly affect a dependent outcome (Y).

Normal Distribution Probability Calculator

Calculate normal distribution cumulative probability and z-scores. Generates right-tailed, left-tailed, and two-tailed bell curve values.

P-Value Calculator

Calculate one-tailed and two-tailed p-values from a Z-score, T-score, F-statistic, or Chi-Square value. Perfect for statistical hypothesis tests.

Percentile Calculator

Calculate the percentile of a value or find values at a specific percentile from any raw data set. Includes step-by-step calculations.

Poisson Distribution Calculator

Calculate the probability of discrete events occurring within a fixed interval using the advanced Poisson mathematical model.

Sample Size Calculator

Calculate the minimum sample size needed for your survey or experiment based on population size, confidence level, and margin of error (with steps/formulas).

T-Distribution Probability Calculator

Calculate the Probability Density Function (PDF) curve height for the Student's t-distribution based on degrees of freedom and specific t-scores.

T-Score Calculator

Standardize small sample data by calculating the t-statistic. Automatically computes the standard error and standard deviation divergence.

T-Test Calculator

Perform an independent two-sample t-test to calculate Welch's t-statistic, standard error, and degrees of freedom for hypothesis testing.

Z-Score Calculator

Convert any raw data point into a Z-score using the population mean and standard deviation. Essential for statistical comparisons across datasets.

Z-Test Calculator

Run a one-sample Z-Test for massive population-scale experimental datasets. Computes the exact Z-Statistic and sample Standard Error.

GPA Calculator

Calculate your grade point average from course grade points and credit hours.

Algebra & Equations

(28)

Antilog Calculator

Calculate antilog instantly for base 10, natural log (e), base 2, or any custom base. See steps, common values, and scientific calculator method.

Arithmetic Sequence Calculator

Use this free Arithmetic Sequence Calculator to find any sequence term, the common difference, or the sum. Shows step-by-step arithmetic formulas.

Completing the Square Calculator

Convert any quadratic equation into vertex form by completing the square. Shows every step so you can find the vertex, axis of symmetry, and check your algebra homework.

Cubic Equation Calculator

Solve ax^3 + bx^2 + cx + d = 0. Find all real and complex cubic roots with Cardano steps, discriminant, and equation breakdown.

Determinant Calculator

Calculate the exact determinant of any 2×2 or 3×3 matrix. Shows the full element-by-element expansion matrix math step by step.

Eigenvalue Calculator

Calculate the eigenvalues of any 2x2 matrix using the characteristic polynomial equation. Shows step-by-step root factoring.

Equation of a Line Calculator

Enter two points and instantly get the slope, y-intercept, and equation in all three standard forms. Shows every calculation step.

Fibonacci Sequence Calculator

Calculate the exact Nth Fibonacci number using Binet's closed-form formula — no slow iteration needed. See the mathematical derivation step by step.

GCF (Greatest Common Factor) Calculator

Find the Greatest Common Factor (GCF) of two or more numbers using the prime factorization or Euclidean algorithm method. Shows full steps.

Geometric Sequence Calculator

Use this free Geometric Sequence Calculator to find the common ratio, nth term, or sum of any geometric sequence. View step-by-step formulas.

Inverse Matrix Calculator

Use this free Inverse Matrix Calculator to find the inverse of a 2x2, 3x3, or 4x4 matrix with step-by-step row operations or determinants.

LCM (Least Common Multiple) Calculator

Find the Least Common Multiple (LCM) of two or more numbers instantly. Essential for adding unlike fractions and finding common denominators.

Logarithm Calculator

Calculate the logarithm of any number for any base. Solve log10, ln (natural log), and log2 equations instantly with step-by-step math.

Matrix Addition Calculator

Add two 2x2 or 3x3 matrices together instantly. Provides clear element-by-element combinatorial breakdowns for linear algebra.

Matrix Multiplication Calculator

Multiply 2x2, 3x3, and larger matrices. View detailed row-by-column calculations and intermediate dot product steps.

Midpoint Formula Calculator

Calculate the midpoint and distance between any two coordinates. Perfect for geometry homework and GPS applications.

Parabola Equation Calculator

Calculate a parabola's standard equation, vertex coordinates, focus, directrix, and axis of symmetry. Shows step-by-step solutions.

Partial Fractions Calculator

Perform partial fraction decomposition on rational expressions with two distinct linear denominators to simplify complex integrals.

Polynomial Factoring Calculator

Use this free Factoring Calculator to factor quadratics, trinomials, and polynomials. View step-by-step solutions using grouping and the AC method.

Prime Factorization Calculator

Decompose any integer into its prime factors with full division steps. See the exact prime factorization tree and exponent notation.

Quadratic Formula Calculator

Solve any quadratic equation instantly. Calculates the discriminant to find real or complex roots, showing every single step of the algebra.

Quartic Equation Calculator

Find all four roots of 4th-degree polynomials simultaneously utilizing the highly robust Durand-Kerner complex iterative algorithm.

Racine Carrée Calculator

Calculate the square root of any positive or negative number instantly. Shows the principal root, imaginary component, and step-by-step simplification.

Slope Calculator

Calculate the slope, y-intercept, and equation of a line passing through two coordinates. Shows step-by-step rise over run math.

Square Calculator

Calculate the perfect square of any number or evaluate base exponents. Includes step-by-step mathematical examples.

Square Root Simplifier

Simplify any square root or radical expression using prime factorization. See exactly how √72 becomes 6√2 with every step shown.

Synthetic Division Calculator

Divide any polynomial by a linear factor (x - c) using the synthetic division shortcut. Instantly find the quotient and remainder.

System of Equations Calculator

Solve any 2×2 system of linear equations using Cramer's Rule. Finds the intersection point or confirms the lines are parallel — with steps.

Geometry & Topology

(43)

Arc Length Calculator

Calculate arc length from radius and central angle, with sector area, chord length, radian conversion, and step-by-step formula output.

Area of Annulus Calculator

Calculate the area of an annulus (the ring between two concentric circles) instantly. Shows step-by-step mathematical workings and formulas.

Area of Circle Calculator

Calculate the area, circumference, diameter, or radius of any circle instantly. Shows standard mathematical steps, formulas, and visual geometry breakdowns.

Area of Circular Sector Calculator

Calculate the area of a circle sector using the radius and central angle. Find the arc length and perimeter with step-by-step mathematical workings.

Area of Circular Segment Calculator

Calculate the area of a circular segment (the region between a chord and an arc). Find the chord length, arc length, and segment height instantly.

Area of Ellipse Calculator

Calculate the area and perimeter of an ellipse. Find the exact surface area and the Ramanujan approximation for the circumference of any oval shape.

Area of Kite Calculator

Calculate the area of a kite using the lengths of its diagonals. Get precise geometric results with a full step-by-step mathematical breakdown.

Area of Parallelogram Calculator

Calculate the area of a parallelogram using base & height, sides & angles, or diagonals. Includes formulas and step-by-step solutions.

Area of Rectangle Calculator

Calculate the area, perimeter, and diagonal of any rectangle instantly. The simplest and fastest geometry tool on the web.

Area of Regular Polygon Calculator

Calculate the area of a regular polygon using the number of sides, side length, or apothem. Includes step-by-step mathematical proofs.

Area of Rhombus Calculator

Use this free Area of a Rhombus Calculator to calculate the area of a rhombus using diagonals or base and height. View step-by-step formulas.

Area of Trapezoid Calculator

Calculate the area of a trapezoid using its bases and height. Find the exact surface area and median length with full step-by-step workings.

Area of Triangle Calculator

Find the area of any triangle using base and height, three sides (Heron's formula), or two sides and angle (SAS). Shows step-by-step solutions.

Centroid of Triangle Calculator

Calculate the centroid of a triangle from its vertex coordinates. Find the geometric center (X, Y) with a full step-by-step breakdown.

Circumference Calculator

Find the circumference of a circle from radius, diameter, or area with instant formulas, steps, diameter, radius, and area outputs.

Circle Equation Calculator

Generate the standard and general form equations for any circle from its center and radius. See full step-by-step mathematical expansion.

Degrees to Radians Converter

Convert degrees to radians or radians to degrees instantly. Shows step-by-step conversions using the pi (π/180) factor.

Distance Formula Calculator

Calculate the Euclidean distance, midpoint, and slope between any two (x, y) coordinates. Shows the full Pythagorean derivation step by step.

Ellipse Equation Calculator

Calculate standard ellipse formulas, area, eccentricity, and Ramanujan's perimeter approximation from the major and minor semi-axes.

Hyperbola Equation Calculator

Find standard hyperbola equation properties including vertices, foci, asymptotes, and eccentricity. Includes step-by-step graph data.

Law of Cosines Calculator

Find missing sides and angles of any triangle using the Law of Cosines. Perfect for non-right triangles where basic trig falls short.

Law of Sines Calculator

Find missing sides and angles using the Law of Sines ratio. Shows the full proportional breakdown for AAS and ASA triangle configurations.

Right Triangle Trigonometry Calculator

Solve a right triangle from its two legs. Find hypotenuse, angles, area, perimeter, sine, cosine, tangent, and step-by-step trig ratios.

Surface Area of Cone Calculator

Instantly calculate the total and lateral surface area of a circular cone using base radius, height, and the Pythagorean slant height derivation.

Surface Area of Cube Calculator

Calculate the total surface area and individual face area of any perfect cube instantly by providing a single edge length measurement.

Surface Area of Cylinder Calculator

Calculate the total and lateral surface area of a cylinder using radius and height. Shows step-by-step cylinder formulas.

Surface Area of Pyramid Calculator

Calculate the total and lateral surface area of any square-based pyramid. View step-by-step calculations using base edge and slant height.

Surface Area of Rectangular Prism Calculator

Calculate the surface area of a rectangular prism or 3D box using length, width, and height. View step-by-step calculations and geometry formulas.

Surface Area of Sphere Calculator

Calculate the exterior surface area of a sphere using radius or diameter. Includes step-by-step calculations with the A = 4πr² formula.

Trigonometric Identity Calculator

Verify the Pythagorean and Double-Angle trigonometric identities by calculating exact sine and cosine ratios for any specific angle input.

Volume of Cone Calculator

Calculate the exact 3D cubic capacity of any standard geometric cone using the radius of its circular base and its perpendicular vertical height.

Volume Calculator

Calculate volume for common 3D shapes including cubes, rectangular prisms, cylinders, cones, spheres, hemispheres, and pyramids.

Volume of Cube Calculator

Calculate the volume of a cube based on its edge length, diagonal, or surface area. Includes step-by-step solutions and formulas.

Volume of Cylinder Calculator

Calculate the volume of any cylinder instantly in liters, gallons, cubic inches, or meters. See the step-by-step formula and geometric math.

Volume of Ellipsoid Calculator

Calculate the internal capacity of asymmetrical, stretched spherical objects by cross-multiplying all three primary dimensional semi-axes.

Volume of Frustum Calculator

Compute the spatial volume of a truncated cone or pyramid frustum. See the step-by-step geometric formulas and structural volume breakdowns.

Volume of Hemisphere Calculator

Instantly calculate the 3D capacity of a perfect hemisphere. Computes exact cubic dimensions based strictly on the equatorial base radius.

Volume of Pyramid Calculator

Compute the spatial volume of any rectangular-based pyramid. Uses fundamental base area and vertical height variables to generate exact capacities.

Volume of Rectangular Prism Calculator

Calculate the volume of a rectangular prism or 3D box using the standard V = lwh formula. Includes step-by-step mathematical expansion.

Volume of Sphere Calculator

Calculate sphere volume from radius, diameter, or circumference with the exact 4/3*pi*r^3 formula, surface area, and step-by-step math.

Volume of Tetrahedron Calculator

Find the exact internal volume of a regular tetrahedron. Accurately evaluates the Platonic solid directly from a single uniform edge length.

Volume of Torus Calculator

Compute the spatial volume of a perfect mathematical torus. Analyzes both minor and major revolutionary radii to output exact cubic capacity.

Volume of Triangular Prism Calculator

Calculate the volume of a triangular prism based on base triangle sides and height. Includes step-by-step geometric breakdowns.

Calculus & Analysis

(14)

Definite Integral Calculator

Use this free Definite Integral Calculator to evaluate integrals with upper and lower bounds. View step-by-step calculus integrations.

Derivative Calculator

Calculate the symbolic derivative of any function instantly. Optionally evaluate the slope at a specific point for tangent line analysis.

Differential Equation Solver

Solve first-order ordinary differential equations (ODEs) numerically using Euler's method. See step-by-step evaluations of dy/dx with custom intervals.

Fourier Series Calculator

Generate the Fourier Series approximation for any continuous mathematical function using high-precision numerical integration.

Implicit Differentiation Calculator

Calculate the implicit derivative dy/dx for complex relational equations where y cannot be isolated. Perfect for multivariable calculus.

Inverse Laplace Transform Calculator

Convert equations from the s-domain back to the time-domain f(t). Includes step-by-step mathematical derivations and lookup tables.

Laplace Transform Calculator

Convert time-domain functions f(t) into the complex frequency s-domain F(s) instantly. Supports polynomials, exponentials, and trig functions.

Limit Calculator

Use this free Limit Calculator to evaluate calculus limit functions. Solve one-sided and two-sided limits instantly with step-by-step proofs.

Maclaurin Series Calculator

Calculate the precise Maclaurin series expansion of any continuous function using symbolic partial derivatives centered at zero.

Multiple Integral Calculator

Use this free Double Integral Calculator to evaluate double and triple integrals. Find step-by-step multiple integrations with bounds.

Partial Derivative Calculator

Compute the symbolic partial derivative of multivariable calculus functions with respect to the variables x, y, or z instantly.

Surface Area of Solid of Revolution Calculator

Perform advanced integral calculus to evaluate the exact surface area generated when a 2D mathematical curve is revolved around an axis.

Taylor Series Calculator

Approximate complex transcendental functions using n-term polynomial Taylor/Maclaurin series expansions centered at a specific coordinate.

Volume of Solid of Revolution Calculator

Evaluate the 3D volume of rotational geometries. Uses the Disk Method and integral calculus to resolve the exact capacity of spun algebraic curves.

Fractions & Proportions

(2)

Equivalent Fractions Calculator

Use this free Equivalent Fractions Calculator to find equivalent fractions (like 18/24, 9/12, or 3/4) with step-by-step simplification proofs.

Simplifying Fractions Calculator

Simplify fractions to their lowest terms instantly. Shows the greatest common divisor (GCD) and step-by-step reduction steps.

Ratios & Rates

(3)

Golden Ratio Calculator

Calculate the Golden Ratio segments for any length. Instantly find the A and B ratios for web design, layout, and art layouts.

Proportion Calculator

Solve any proportion equation by finding the missing value. Cross-multiply and verify proportional relationships step by step.

Ratio Calculator

Simplify, scale, and compare ratios instantly. Find equivalent ratios, missing values, and reduce any ratio to its simplest form.

Percentages

(4)

Percentage Change Calculator

Calculate the percentage change, increase, or decrease between two numbers. Ideal for tracking price changes, wage changes, and stock value fluctuations with steps.

Percentage Difference Calculator

Calculate the true percentage difference between two values using the average-based formula. Confused about % difference vs % change vs % error? We explain exactly when to use each one — with step-by-step workings.

Percentage Error Calculator

Use this free Percent Error Calculator to calculate the percent error between experimental and theoretical values. View step-by-step math steps.

Percentage Calculator

Calculate percentage change, percentage difference, or percentage error between two numbers with clear step-by-step results.

Scientific Notation

(3)

Scientific Notation Calculator

Convert numbers to and from scientific notation, decimal notation, and engineering notation. See step-by-step mathematical breakdowns.

Significant Figures Calculator

Round numbers to significant figures and estimate original sig figs. Shows scientific notation, leading/trailing zero rules, and calculation steps.

Scientific Calculator

Run common scientific calculator operations including powers, square roots, logarithms, trigonometry, and arithmetic.

Math Calculators for Algebra, Geometry & Statistics

Use this math calculator library to solve the exact type of problem in front of you: algebra equations, geometry measurements, statistics tests, calculus operations, fractions, ratios, percentages, and scientific notation. Each tool is built for fast answer checking and formula review.

For high-demand geometry answers, start with the volume calculator, volume of a sphere calculator, arc length calculator, and circumference calculator. If your problem involves triangle angles, the right triangle trigonometry calculator connects the geometry and trig formulas directly.

The calculators are designed for students, teachers, engineers, and anyone who needs a reliable way to verify work. Many tools show intermediate steps, formulas, and notation so you can understand how the final answer was produced.

Core Mathematics Categories:
• Algebra & Equations: Solve linear, quadratic, and cubic equations, factor polynomials, and invert matrices.
• Geometry: Calculate area, perimeter, volume, and surface area for circles, spheres, cylinders, and complex polyhedra.
• Statistics & Probability: Find mean, median, mode, standard deviation, and evaluate probability distributions like normal and binomial.
• Calculus: Compute derivatives, evaluate double and triple integrals, and solve ordinary differential equations.

Verify your answers and speed up your workflow with Babbage Calculator.

Frequently Asked Questions

Yes! The majority of our mathematics, algebra, and geometry calculators feature detailed step-by-step explanations, showing you exactly how the final formula is solved.

Absolutely. Our tools are designed to help students check their answers, understand intermediate steps, and learn standard mathematical methods.

No. All computations are run locally using standard math libraries, handling complex variables, fractions, and large numbers instantly.