Mathematical Formulas & Calculators
Complete collection of 120 formulas with examples and interactive calculators
Statistics
Mean (Average) Formula - Statistics
Learn the mean (average) formula with examples, step-by-step guide, and calculator tools. Calculate the arithmetic mean (average) of a dataset
Variance Formula - Statistics
Learn the variance formula with examples, step-by-step guide, and calculator tools. Measure how far a set of numbers are spread out from their average
Standard Deviation Formula - Statistics
Learn the standard deviation formula with examples, step-by-step guide, and calculator tools. Measure the amount of variation in a set of values
Median Formula - Statistics
Learn the median formula with examples, step-by-step guide, and calculator tools. Find the middle value in a sorted dataset
Mode Formula - Statistics
Learn the mode formula with examples, step-by-step guide, and calculator tools. Find the most frequently occurring value in a dataset
Z-Score Formula - Statistics
Learn the z-score formula with examples, step-by-step guide, and calculator tools. Calculate how many standard deviations a value is from the mean
Percentile Formula - Statistics
Learn the percentile formula with examples, step-by-step guide, and calculator tools. Calculate the position of a value in a percentile ranking
Quartile Formula - Statistics
Learn the quartile formula with examples, step-by-step guide, and calculator tools. Divide a dataset into four equal parts
Range Formula - Statistics
Learn the range formula with examples, step-by-step guide, and calculator tools. Calculate the difference between the largest and smallest values
Interquartile Range (IQR) Formula - Statistics
Learn the interquartile range (iqr) formula with examples, step-by-step guide, and calculator tools. Measure the spread of the middle 50% of data
Coefficient of Variation Formula - Statistics
Learn the coefficient of variation formula with examples, step-by-step guide, and calculator tools. Measure relative variability as a percentage
Skewness Formula - Statistics
Learn the skewness formula with examples, step-by-step guide, and calculator tools. Measure the asymmetry of a probability distribution
Kurtosis Formula - Statistics
Learn the kurtosis formula with examples, step-by-step guide, and calculator tools. Measure the tailedness of a probability distribution
Correlation Coefficient Formula - Statistics
Learn the correlation coefficient formula with examples, step-by-step guide, and calculator tools. Measure the strength and direction of linear relationship between two variables
Linear Regression Formula - Statistics
Learn the linear regression formula with examples, step-by-step guide, and calculator tools. Find the best-fit line through a set of points
Sample Variance - Statistics
Learn the sample variance with examples, step-by-step guide, and calculator tools. Variance of sample data
T-Statistic - Statistics
Learn the t-statistic with examples, step-by-step guide, and calculator tools. Test statistic for t-test
Chi-Square Statistic - Statistics
Learn the chi-square statistic with examples, step-by-step guide, and calculator tools. Test for categorical data
ANOVA F-Statistic - Statistics
Learn the anova f-statistic with examples, step-by-step guide, and calculator tools. Test for equality of means
Regression Coefficient - Statistics
Learn the regression coefficient with examples, step-by-step guide, and calculator tools. Slope in linear regression
R-Squared (Coefficient of Determination) - Statistics
Learn the r-squared (coefficient of determination) with examples, step-by-step guide, and calculator tools. Proportion of variance explained
Standard Error of Mean - Statistics
Learn the standard error of mean with examples, step-by-step guide, and calculator tools. Standard deviation of sample mean
Margin of Error - Statistics
Learn the margin of error with examples, step-by-step guide, and calculator tools. Range of uncertainty in estimate
Confidence Interval for Mean - Statistics
Learn the confidence interval for mean with examples, step-by-step guide, and calculator tools. Range likely to contain population mean
Pooled Variance - Statistics
Learn the pooled variance with examples, step-by-step guide, and calculator tools. Combined variance from two samples
Probability
Binomial Probability Formula - Probability
Learn the binomial probability formula with examples, step-by-step guide, and calculator tools. Calculate probability of k successes in n independent trials
Normal Distribution Formula - Probability
Learn the normal distribution formula with examples, step-by-step guide, and calculator tools. Calculate probability density for normal distribution
Poisson Distribution Formula - Probability
Learn the poisson distribution formula with examples, step-by-step guide, and calculator tools. Calculate probability of k events in a fixed interval
Conditional Probability Formula - Probability
Learn the conditional probability formula with examples, step-by-step guide, and calculator tools. Calculate probability of A given that B has occurred
Bayes' Theorem Formula - Probability
Learn the bayes' theorem formula with examples, step-by-step guide, and calculator tools. Calculate posterior probability using prior probability and likelihood
Algebra
Quadratic Formula - Algebra
Learn the quadratic formula with examples, step-by-step guide, and calculator tools. Solve quadratic equations of the form ax² + bx + c = 0
Slope Formula - Algebra
Learn the slope formula with examples, step-by-step guide, and calculator tools. Calculate the slope of a line through two points
Distance Formula - Algebra
Learn the distance formula with examples, step-by-step guide, and calculator tools. Calculate distance between two points in a plane
Midpoint Formula - Algebra
Learn the midpoint formula with examples, step-by-step guide, and calculator tools. Find the middle point between two coordinates
Point-Slope Form Formula - Algebra
Learn the point-slope form formula with examples, step-by-step guide, and calculator tools. Equation of a line given a point and slope
Geometry
Circle Area Formula - Geometry
Learn the circle area formula with examples, step-by-step guide, and calculator tools. Calculate the area of a circle
Circle Circumference Formula - Geometry
Learn the circle circumference formula with examples, step-by-step guide, and calculator tools. Calculate the circumference of a circle
Triangle Area Formula - Geometry
Learn the triangle area formula with examples, step-by-step guide, and calculator tools. Calculate the area of a triangle
Pythagorean Theorem - Geometry
Learn the pythagorean theorem with examples, step-by-step guide, and calculator tools. Relate the lengths of sides in a right triangle
Rectangle Area Formula - Geometry
Learn the rectangle area formula with examples, step-by-step guide, and calculator tools. Calculate the area of a rectangle
Finance
Compound Interest Formula - Finance
Learn the compound interest formula with examples, step-by-step guide, and calculator tools. Calculate future value with compound interest
Simple Interest Formula - Finance
Learn the simple interest formula with examples, step-by-step guide, and calculator tools. Calculate simple interest on a loan or investment
Mortgage Payment Formula - Finance
Learn the mortgage payment formula with examples, step-by-step guide, and calculator tools. Calculate monthly mortgage payment
Present Value Formula - Finance
Learn the present value formula with examples, step-by-step guide, and calculator tools. Calculate present value of a future amount
Future Value Formula - Finance
Learn the future value formula with examples, step-by-step guide, and calculator tools. Calculate future value of an investment
Calculus
Power Rule for Derivatives - Calculus
Learn the power rule for derivatives with examples, step-by-step guide, and calculator tools. Differentiate power functions
Chain Rule - Calculus
Learn the chain rule with examples, step-by-step guide, and calculator tools. Differentiate composite functions
Product Rule - Calculus
Learn the product rule with examples, step-by-step guide, and calculator tools. Differentiate product of two functions
Quotient Rule - Calculus
Learn the quotient rule with examples, step-by-step guide, and calculator tools. Differentiate quotient of two functions
Power Rule for Integrals - Calculus
Learn the power rule for integrals with examples, step-by-step guide, and calculator tools. Integrate power functions
Limit Definition - Calculus
Learn the limit definition with examples, step-by-step guide, and calculator tools. Formal definition of a limit
Derivative Definition - Calculus
Learn the derivative definition with examples, step-by-step guide, and calculator tools. Fundamental definition of derivative
Sum Rule for Derivatives - Calculus
Learn the sum rule for derivatives with examples, step-by-step guide, and calculator tools. Derivative of sum is sum of derivatives
Exponential Derivative - Calculus
Learn the exponential derivative with examples, step-by-step guide, and calculator tools. Derivative of exponential function
Logarithm Derivative - Calculus
Learn the logarithm derivative with examples, step-by-step guide, and calculator tools. Derivative of natural logarithm
Sine Derivative - Calculus
Learn the sine derivative with examples, step-by-step guide, and calculator tools. Derivative of sine function
Cosine Derivative - Calculus
Learn the cosine derivative with examples, step-by-step guide, and calculator tools. Derivative of cosine function
Definite Integral - Calculus
Learn the definite integral with examples, step-by-step guide, and calculator tools. Calculate area under curve between limits
Fundamental Theorem of Calculus - Calculus
Learn the fundamental theorem of calculus with examples, step-by-step guide, and calculator tools. Links differentiation and integration
Integration by Parts - Calculus
Learn the integration by parts with examples, step-by-step guide, and calculator tools. Method for integrating products
Partial Derivative - Calculus
Learn the partial derivative with examples, step-by-step guide, and calculator tools. Derivative with respect to one variable
Gradient Vector - Calculus
Learn the gradient vector with examples, step-by-step guide, and calculator tools. Vector of all partial derivatives
Taylor Series - Calculus
Learn the taylor series with examples, step-by-step guide, and calculator tools. Infinite series representation of function
Maclaurin Series - Calculus
Learn the maclaurin series with examples, step-by-step guide, and calculator tools. Taylor series centered at zero
L'Hôpital's Rule - Calculus
Learn the l'hôpital's rule with examples, step-by-step guide, and calculator tools. Evaluate indeterminate limits
Trigonometry
Sine Function - Trigonometry
Learn the sine function with examples, step-by-step guide, and calculator tools. Calculate the sine of an angle in a right triangle
Cosine Function - Trigonometry
Learn the cosine function with examples, step-by-step guide, and calculator tools. Calculate the cosine of an angle in a right triangle
Tangent Function - Trigonometry
Learn the tangent function with examples, step-by-step guide, and calculator tools. Calculate the tangent of an angle
Law of Sines - Trigonometry
Learn the law of sines with examples, step-by-step guide, and calculator tools. Relate sides and angles in any triangle
Law of Cosines - Trigonometry
Learn the law of cosines with examples, step-by-step guide, and calculator tools. Relate all three sides and one angle in a triangle
Pythagorean Identity - Trigonometry
Learn the pythagorean identity with examples, step-by-step guide, and calculator tools. Fundamental trigonometric identity
Double Angle Formula (Sine) - Trigonometry
Learn the double angle formula (sine) with examples, step-by-step guide, and calculator tools. Express sine of double angle
Double Angle Formula (Cosine) - Trigonometry
Learn the double angle formula (cosine) with examples, step-by-step guide, and calculator tools. Express cosine of double angle
Sum of Angles (Sine) - Trigonometry
Learn the sum of angles (sine) with examples, step-by-step guide, and calculator tools. Sine of sum of two angles
Sum of Angles (Cosine) - Trigonometry
Learn the sum of angles (cosine) with examples, step-by-step guide, and calculator tools. Cosine of sum of two angles
Inverse Sine (Arcsine) - Trigonometry
Learn the inverse sine (arcsine) with examples, step-by-step guide, and calculator tools. Find angle from sine value
Inverse Cosine (Arccosine) - Trigonometry
Learn the inverse cosine (arccosine) with examples, step-by-step guide, and calculator tools. Find angle from cosine value
Inverse Tangent (Arctangent) - Trigonometry
Learn the inverse tangent (arctangent) with examples, step-by-step guide, and calculator tools. Find angle from tangent value
Secant Function - Trigonometry
Learn the secant function with examples, step-by-step guide, and calculator tools. Reciprocal of cosine
Cosecant Function - Trigonometry
Learn the cosecant function with examples, step-by-step guide, and calculator tools. Reciprocal of sine
Physics
Newton's Second Law - Physics
Learn the newton's second law with examples, step-by-step guide, and calculator tools. Force equals mass times acceleration
Kinetic Energy - Physics
Learn the kinetic energy with examples, step-by-step guide, and calculator tools. Energy of motion
Gravitational Potential Energy - Physics
Learn the gravitational potential energy with examples, step-by-step guide, and calculator tools. Energy due to height
Work-Energy Theorem - Physics
Learn the work-energy theorem with examples, step-by-step guide, and calculator tools. Work done by force
Power Formula - Physics
Learn the power formula with examples, step-by-step guide, and calculator tools. Rate of doing work
Momentum - Physics
Learn the momentum with examples, step-by-step guide, and calculator tools. Quantity of motion
Impulse-Momentum Theorem - Physics
Learn the impulse-momentum theorem with examples, step-by-step guide, and calculator tools. Change in momentum
Ohm's Law - Physics
Learn the ohm's law with examples, step-by-step guide, and calculator tools. Relationship between voltage, current, and resistance
Wave Speed - Physics
Learn the wave speed with examples, step-by-step guide, and calculator tools. Speed of wave propagation
Ideal Gas Law - Physics
Learn the ideal gas law with examples, step-by-step guide, and calculator tools. Behavior of ideal gas
Chemistry
Molarity - Chemistry
Learn the molarity with examples, step-by-step guide, and calculator tools. Concentration in moles per liter
Avogadro's Number - Chemistry
Learn the avogadro's number with examples, step-by-step guide, and calculator tools. Number of particles in a mole
pH Formula - Chemistry
Learn the ph formula with examples, step-by-step guide, and calculator tools. Measure of acidity
Dilution Formula - Chemistry
Learn the dilution formula with examples, step-by-step guide, and calculator tools. Relationship in dilution
Percent Yield - Chemistry
Learn the percent yield with examples, step-by-step guide, and calculator tools. Efficiency of chemical reaction
Boyle's Law - Chemistry
Learn the boyle's law with examples, step-by-step guide, and calculator tools. Pressure-volume relationship at constant temperature
Charles' Law - Chemistry
Learn the charles' law with examples, step-by-step guide, and calculator tools. Volume-temperature relationship at constant pressure
Rate Law - Chemistry
Learn the rate law with examples, step-by-step guide, and calculator tools. Reaction rate dependence on concentration
Arrhenius Equation - Chemistry
Learn the arrhenius equation with examples, step-by-step guide, and calculator tools. Temperature dependence of reaction rate
Gibbs Free Energy - Chemistry
Learn the gibbs free energy with examples, step-by-step guide, and calculator tools. Spontaneity of reaction
Linear Algebra
Matrix Addition - Linear Algebra
Learn the matrix addition with examples, step-by-step guide, and calculator tools. Add corresponding elements
Matrix Multiplication - Linear Algebra
Learn the matrix multiplication with examples, step-by-step guide, and calculator tools. Multiply matrices using dot product
2×2 Matrix Determinant - Linear Algebra
Learn the 2×2 matrix determinant with examples, step-by-step guide, and calculator tools. Calculate determinant of 2×2 matrix
2×2 Matrix Inverse - Linear Algebra
Learn the 2×2 matrix inverse with examples, step-by-step guide, and calculator tools. Inverse of 2×2 matrix
Matrix Transpose - Linear Algebra
Learn the matrix transpose with examples, step-by-step guide, and calculator tools. Flip matrix over diagonal
Dot Product - Linear Algebra
Learn the dot product with examples, step-by-step guide, and calculator tools. Scalar product of vectors
Cross Product - Linear Algebra
Learn the cross product with examples, step-by-step guide, and calculator tools. Vector product perpendicular to both vectors
Vector Magnitude - Linear Algebra
Learn the vector magnitude with examples, step-by-step guide, and calculator tools. Length of vector
Eigenvalue Equation - Linear Algebra
Learn the eigenvalue equation with examples, step-by-step guide, and calculator tools. Vector scaled by matrix
Gram-Schmidt Process - Linear Algebra
Learn the gram-schmidt process with examples, step-by-step guide, and calculator tools. Orthogonalize vectors
Number Theory
Factorial - Number Theory
Learn the factorial with examples, step-by-step guide, and calculator tools. Product of all positive integers up to n
Permutations - Number Theory
Learn the permutations with examples, step-by-step guide, and calculator tools. Number of ways to arrange r items from n
Combinations - Number Theory
Learn the combinations with examples, step-by-step guide, and calculator tools. Number of ways to choose r items from n
Fibonacci Formula (Binet) - Number Theory
Learn the fibonacci formula (binet) with examples, step-by-step guide, and calculator tools. Direct formula for Fibonacci numbers
Golden Ratio - Number Theory
Learn the golden ratio with examples, step-by-step guide, and calculator tools. Mathematical constant appearing in nature
Prime Number Theorem - Number Theory
Learn the prime number theorem with examples, step-by-step guide, and calculator tools. Approximate number of primes less than x
Euler's Totient Function - Number Theory
Learn the euler's totient function with examples, step-by-step guide, and calculator tools. Count of integers coprime to n
Divisor Function - Number Theory
Learn the divisor function with examples, step-by-step guide, and calculator tools. Sum of divisors of n
Greatest Common Divisor - Number Theory
Learn the greatest common divisor with examples, step-by-step guide, and calculator tools. Euclidean algorithm for GCD
Least Common Multiple - Number Theory
Learn the least common multiple with examples, step-by-step guide, and calculator tools. Smallest multiple of both numbers