Arithmetic Fundamentals
The foundation of all mathematics, arithmetic covers basic operations with numbers. Master these fundamental concepts to build a strong mathematical foundation.
Basic Operations
Understanding addition, subtraction, multiplication, and division with integers, fractions, and decimals.
Fractions & Percentages
Working with rational numbers, percentages, ratios, and proportional relationships.
Exponents & Roots
Working with powers, exponents, square roots, and scientific notation.
Interactive Example: Percentage Calculation
Problem: Calculate 25% of 80 and find what percentage 20 is of 80.
Part = (Percentage / 100) ร Whole
Percentage = (Part / Whole) ร 100
Solution:
1. 25% of 80 = (25/100) ร 80 = 0.25 ร 80 = 20
2. 20 is what percentage of 80? = (20/80) ร 100 = 0.25 ร 100 = 25%
Try Related Calculators
Apply your arithmetic knowledge with our specialized calculators:
Basic Calculator
Perform basic operations
Percentage Calculator
Calculate percentages
Average Calculator
Calculate the average of a set of numbers
Fraction Calculator
Work with fractions
Rounding Calculator
Round numbers to a specified precision
Factorial Calculator
Calculate the factorial of a number
Division Calculator
Perform division operations
Ratio Calculator
Calculate ratios and proportions
Scientific Calculator
Perform advanced mathematical operations
Algebra & Equations
Algebra is the language of mathematics. Learn to solve equations, work with variables, and understand functional relationships between quantities.
Linear Algebra
Solving linear equations, working with variables, and understanding algebraic expressions.
Polynomials & Functions
Working with polynomial expressions, quadratic equations, and various function types.
Advanced Algebra
Complex algebraic concepts including matrices, sequences, and advanced equations.
Quadratic Formula Example
Problem: Solve the quadratic equation: xยฒ + 5x + 6 = 0
For equation: axยฒ + bx + c = 0
Solutions: x = [-b ยฑ โ(bยฒ - 4ac)] / 2a
Solution:
1. Identify coefficients: a = 1, b = 5, c = 6
2. Calculate discriminant: bยฒ - 4ac = 25 - 24 = 1
3. Apply formula: x = [-5 ยฑ โ1] / 2
4. Solutions: x = (-5 + 1)/2 = -2 and x = (-5 - 1)/2 = -3
Equation Solver
Solve algebraic equations step-by-step with accurate solutions
Quadratic Formula
Find roots of quadratic equations using the quadratic formula
Matrix Calculator
Perform matrix addition, multiplication, inverse, and determinant
Exponent Calculator
Calculate powers, exponents, and exponential expressions
Function Calculator
Evaluate mathematical functions and solve function expressions
Inequality Calculator
Solve linear and quadratic inequalities with step-by-step solutions
Log Calculator
Calculate logarithms, log base values, and log equations instantly
Polynomial Calculator
Simplify, factor, and solve polynomial expressions
Root Calculator
Find square roots, cube roots, and nth roots of numbers
Slope Calculator
Calculate slope, gradient, and line equation from given points
Geometry & Shapes
The study of shapes, sizes, relative positions, and properties of space. Geometry deals with points, lines, angles, surfaces, and solids.
Plane Geometry
Two-dimensional shapes and their properties in a flat plane.
Solid Geometry
Three-dimensional shapes and their properties in space.
Geometric Measurement
Calculating dimensions, areas, perimeters, and volumes of geometric shapes.
Triangle Area Example
Problem: Find the area of a triangle with base 10 units and height 6 units.
Area = ยฝ ร base ร height
A = ยฝ ร b ร h
Solution:
1. Identify values: base (b) = 10 units, height (h) = 6 units
2. Apply formula: Area = ยฝ ร 10 ร 6
3. Calculate: Area = 5 ร 6 = 30 square units
Triangle Calculator
Calculate triangle sides, angles, area, and perimeter ุจุณูููุฉ
Circle Calculator
Find radius, diameter, circumference, and area of a circle
Area Calculator
Calculate area of shapes like squares, rectangles, triangles, and circles
Coordinate Geometry Calculator
Calculate distance, midpoint, and slope between coordinate points
Distance Calculator
Find distance between two points using distance formula
Perimeter Calculator
Calculate perimeter of geometric shapes quickly and accurately
Polygon Calculator
Calculate polygon area, sides, angles, and perimeter
Pythagorean Theorem Calculator
Find missing sides of right triangles using Pythagorean theorem
Right Triangle Calculator
Calculate sides, angles, and area of right triangles ุจุณูููุฉ
Trigonometry Calculator
Calculate sine, cosine, tangent, and trigonometric values
Calculus & Analysis
The mathematical study of continuous change, focusing on derivatives (rates of change) and integrals (accumulation of quantities).
Differential Calculus
Study of derivatives and their applications to rates of change and slopes of curves.
Integral Calculus
Study of integrals and their applications to areas, volumes, and accumulation.
Multivariable Calculus
Extension of calculus to functions of multiple variables.
Derivative Example
Problem: Find the derivative of f(x) = 3xยฒ + 2x - 5
d/dx [xโฟ] = nยทxโฟโปยน
d/dx [constant] = 0
Solution:
1. Apply power rule to 3xยฒ: 2 ร 3xยฒโปยน = 6x
2. Apply power rule to 2x: 1 ร 2xยนโปยน = 2
3. Derivative of constant -5: 0
4. Combine: f'(x) = 6x + 2
Derivative Calculator
Compute derivatives of functions step-by-step with accurate solutions
Integral Calculator
Calculate definite and indefinite integrals of functions easily
Limit Calculator
Find limits of functions as variables approach specific values
Arc Length Calculator
Calculate the length of curves and arcs using calculus formulas
Area Under Curve Calculator
Compute the area under curves using definite integrals
Differential Calculator
Calculate differentials and derivatives of functions easily
Double Integral Calculator
Evaluate double integrals over regions in 2D space
Fourier Calculator
Compute Fourier series and Fourier transforms of functions
Gradient Calculator
Calculate the gradient vector and directional derivatives
Partial Derivative Calculator
Compute partial derivatives of multivariable functions
PDE Calculator
Solve partial differential equations step-by-step
Surface Area Calculator
Calculate surface areas of solids using calculus formulas
Taylor Series Calculator
Compute Taylor series expansions of functions at a point
Triple Integral Calculator
Evaluate triple integrals over 3D regions accurately
Volume Calculator
Calculate volumes of solids using integrals and geometry
Statistics & Probability
The science of collecting, analyzing, interpreting, presenting, and organizing data. Probability deals with the likelihood of events occurring.
Descriptive Statistics
Methods for summarizing and describing the main features of data collections.
Probability
The mathematics of chance and uncertainty, quantifying how likely events are to occur.
Inferential Statistics
Making predictions or inferences about a population based on sample data.
Standard Deviation Example
Problem: Calculate standard deviation for dataset: [2, 4, 4, 4, 5, 5, 7, 9]
ฯ = โ[ฮฃ(xแตข - ฮผ)ยฒ / N]
Where ฮผ = mean, N = number of values
Solution:
1. Calculate mean: (2+4+4+4+5+5+7+9)/8 = 40/8 = 5
2. Calculate squared differences: (2-5)ยฒ=9, (4-5)ยฒ=1, etc.
3. Sum squared differences: 9+1+1+1+0+0+4+16 = 32
4. Divide by N: 32/8 = 4
5. Square root: โ4 = 2
Mean/Median/Mode Calculator
Calculate the mean, median, and mode of datasets accurately
Standard Deviation Calculator
Measure data dispersion using standard deviation calculations
Probability Calculator
Compute probabilities for events using various distributions
ANOVA Calculator
Perform analysis of variance to compare group means statistically
Confidence Interval Calculator
Calculate confidence intervals for population parameters
Correlation Calculator
Determine the correlation coefficient between two datasets
Descriptive Statistics Calculator
Compute summary statistics including mean, median, mode, and range
Hypothesis Testing Calculator
Test statistical hypotheses with t-tests, z-tests, and more
p-value Calculator
Calculate p-values to assess statistical significance of results
Regression Analysis Calculator
Perform linear and multiple regression analysis for datasets
Sample Size Calculator
Determine the required sample size for accurate statistical results
t-test Calculator
Conduct t-tests to compare means between two groups
z-score Calculator
Compute z-scores to determine standard deviations from the mean
Number Theory
The branch of mathematics devoted to the study of integers and integer-valued functions, focusing on properties and relationships of numbers.
Divisibility & Primes
Study of divisibility properties, prime numbers, and their fundamental properties.
Modular Arithmetic
Arithmetic system for integers where numbers "wrap around" upon reaching a certain value.
Special Numbers
Study of special classes of numbers with unique properties and applications.
Prime Factorization Example
Problem: Find the prime factorization of 84
Divide by smallest primes until only 1 remains
Express result as product of prime factors
Solution:
1. Divide by 2: 84 รท 2 = 42
2. Divide by 2: 42 รท 2 = 21
3. Divide by 3: 21 รท 3 = 7
4. 7 is prime: 7 รท 7 = 1
5. Prime factorization: 84 = 2 ร 2 ร 3 ร 7 = 2ยฒ ร 3 ร 7
Prime Factorization Calculator
Break down numbers into their prime factors accurately
GCF Calculator
Find the greatest common divisor of two or more numbers
LCM Calculator
Calculate the least common multiple of numbers easily
Common Factor Calculator
Identify common factors of given numbers quickly
Divisibility Calculator
Check if a number is divisible by another number
Euler's Totient Calculator
Compute Euler's totient function for a given integer
Factor Calculator
Find all factors of a given number efficiently
Fraction Simplifier
Simplify fractions to their lowest terms instantly
Modulo Calculator
Calculate the remainder of a division operation using modulo
Number Properties Calculator
Analyze properties of numbers including even, odd, prime, and more
Prime Number Calculator
Identify whether a number is prime and list prime numbers
Trigonometry
The study of relationships between angles and sides of triangles, with applications to periodic phenomena and circular motion.
Trigonometric Functions
Understanding sine, cosine, tangent, and their reciprocal functions.
Trigonometric Identities
Mathematical equations involving trigonometric functions that are true for all values.
Trigonometric Equations
Solving equations involving trigonometric functions and their applications.
Right Triangle Example
Problem: In a right triangle, angle A = 30ยฐ, hypotenuse = 10. Find opposite side.
sin(ฮธ) = Opposite / Hypotenuse
Opposite = Hypotenuse ร sin(ฮธ)
Solution:
1. Identify known: ฮธ = 30ยฐ, Hypotenuse = 10
2. sin(30ยฐ) = 0.5
3. Opposite = 10 ร 0.5 = 5
4. The opposite side is 5 units
Linear Algebra
The study of vectors, vector spaces, linear transformations, and systems of linear equations. Fundamental to modern mathematics and its applications.
Vectors & Spaces
Understanding vectors, vector spaces, and their properties in multiple dimensions.
Matrices
Working with matrices, their operations, and applications to linear systems.
Linear Transformations
Understanding linear transformations, eigenvalues, and eigenvectors.
Matrix Multiplication Example
Problem: Multiply matrices A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]]
C[i][j] = ฮฃ A[i][k] ร B[k][j]
Sum over k from 1 to n
Solution:
1. C[1][1] = (1ร5) + (2ร7) = 5 + 14 = 19
2. C[1][2] = (1ร6) + (2ร8) = 6 + 16 = 22
3. C[2][1] = (3ร5) + (4ร7) = 15 + 28 = 43
4. C[2][2] = (3ร6) + (4ร8) = 18 + 32 = 50
5. Result: [[19, 22], [43, 50]]
Your Learning Journey
Follow this structured path to master mathematics systematically
Master Fundamentals
Start with arithmetic operations, fractions, decimals, and percentages. Build a strong foundation for all mathematical concepts.
Learn Algebra
Understand variables, equations, and functions. Master solving techniques for linear and quadratic equations.
Explore Geometry
Study shapes, sizes, and spatial relationships. Learn to calculate areas, volumes, and understand geometric proofs.
Advance to Calculus
Master limits, derivatives, and integrals. Understand rates of change and accumulation in continuous systems.
Apply Statistics
Learn data analysis, probability, and statistical inference. Apply mathematical concepts to real-world data.
Ready to Master Mathematics?
Combine theoretical knowledge with practical application using our comprehensive calculator tools. Get instant solutions with detailed step-by-step explanations.