Mathematics Tutorials, Formulas, and Calculators

This mathematics learning hub brings together calculators, formulas, worked methods, and concept guides across arithmetic, geometry, fractions, polynomials, vectors, algebra, matrices, trigonometry, and calculus. Select a topic below to review a definition, apply a formula, or solve a calculation step by step.

Arithmetic Calculators and Number Skills

Arithmetic covers number relationships, factors, comparisons, sequences, and fraction equivalence. Use these calculators when you need to simplify a calculation or verify a numerical result.

  1. Equivalent Fractions Calculator
  2. GCD Calculator
  3. GCF Calculator
  4. Geometric Sequence Calculator
  5. Greater Than or Less Than Calculator

Geometry Calculators and Shape Formulas

Geometry studies the size, shape, position, and properties of figures. The following calculators cover common two-dimensional shapes and help you find measurements such as area, perimeter, circumference, and related dimensions.

Circle and Quadrilateral Calculators

  1. Circle Calculator
  2. Semi-Circle Calculator
  3. Square Calculator
  4. Rectangle Calculator
  5. Rhombus Calculator
  6. Parallelogram Calculator

Triangle Formulas and Area Methods

A triangle can be solved in different ways depending on the information given. Start with the basic perimeter and area formulas, then choose the method that matches the known side lengths or angles.

Triangle Formula References
  1. Perimeter of a Triangle Formula
  2. Area of a Triangle Formula
How to Find the Area of a Triangle
  1. How to find the Area of a Triangle given Three Sides Lengths?
  2. How to find the Area of a Triangle given Lengths of Two Sides and the Included Angle?
  3. How to find the Area of a Triangle given the Length of a Side and the Two Angles on its edges?
  4. How to find the Area of a Right-Angled Triangle given lengths of Base and Height?
  5. How to find the Area of a Right-Angled Triangle given Base and an Angle?

Trigonometry Ratios, Identities, and Graphs

Trigonometry connects angles with side-length ratios, especially in right triangles. It is also used to model periodic behavior through sine, cosine, tangent, and their reciprocal functions.

  1. What is Trigonometry?
  2. Applications of Trigonometry in Real Life
Six Trigonometric Ratios
  1. Sine (sin)
  2. Cosine (cos)
  3. Tangent (tan)
  4. Cosecant (csc)
  5. Secant (sec)
  6. Cotangent (cot)
Trigonometric Identities and Equations
  1. Reciprocal Identities
  2. Pythagorean Identities
  3. Trigonometric Identities and Equations
Graphs of Trigonometric Functions
  1. Graph of Sine Function
  2. Graph of Cosine Function
  3. Graph of Tangent Function
  4. Graph of Cosecant Function
  5. Graph of Secant Function
  6. Graph of Cotangent Function
  7. Properties of Trigonometric Graphs

Fraction Conversion and Simplification

Fractions represent parts of a whole or ratios between quantities. Use the calculator below to convert an improper fraction into a mixed number while keeping the value unchanged.

  1. Improper Fraction to Mixed Number Calculator

Polynomial Addition and Subtraction

Polynomials are algebraic expressions made from variables, coefficients, and non-negative integer exponents. When adding or subtracting polynomials, combine only like terms with the same variables and exponents.

  1. Adding and Subtracting Polynomials Calculator

Vector Cross Product Calculator

Vectors have both magnitude and direction. The cross product of two three-dimensional vectors produces a vector perpendicular to both original vectors, with direction determined by the right-hand rule.

  1. Vector Cross Product Calculator

Algebra and Linear Equations

Algebra uses symbols to represent unknown or variable quantities. Linear equations are equations in which each variable has an exponent of one, and their solutions can be found by applying the same valid operation to both sides.

  1. Linear Equations

Matrices, Matrix Types, and Operations

A matrix is a rectangular arrangement of values in rows and columns. Begin with the matrix overview, review the common matrix types, and then study addition, subtraction, and multiplication.

Matrix Definitions and Types

  1. Matrix
  2. Types of Matrices
  3. Row Matrix
  4. Column Matrix
  5. Square Matrix
  6. Diagonal Matrix
  7. Scalar Matrix
  8. Identity Matrix
  9. Zero Matrix
  10. Upper Triangular Matrix
  11. Lower Triangular Matrix
  12. Symmetric Matrix
  13. Skew-Symmetric Matrix
  14. Singular Matrix
  15. Non-Singular Matrix

Matrix Addition, Subtraction, and Multiplication

  1. Matrix Addition
  2. Matrix Subtraction
  3. Matrix Multiplication

For matrix addition and subtraction, the matrices must have the same dimensions. For matrix multiplication, the number of columns in the first matrix must equal the number of rows in the second matrix.

Calculus Topics: Limits, Integration, and Differential Equations

Calculus studies change and accumulation. Limits describe the value a function approaches, integration measures accumulated quantities, and differential equations relate an unknown function to one or more of its derivatives.

  1. Differential Equations
  2. Integration
  3. Limits

How to Choose the Right Mathematics Resource

  • Use a calculator when you need a quick numerical result or want to verify manual work.
  • Use a formula guide when the required measurements are known but you need the correct relationship between them.
  • Use a how-to tutorial when the solution depends on several steps or on selecting a method from the available information.
  • Use a concept article when you need definitions, properties, notation, and conditions before solving problems.

Mathematics Page Editorial QA Checklist

  • Confirm that every formula states what each symbol represents.
  • Check that units are consistent before substituting values.
  • Verify calculator inputs, rounding rules, and output labels.
  • Ensure triangle methods match the given sides and angles.
  • Confirm matrix dimensions satisfy the selected operation.
  • Recalculate worked examples independently before publication.