Advanced Scientific Calculator

Calculator

Matrix

Probability

Area & Volume

Statistics

Calculus

Engineering

Physics

Finance

Equations

Basic Calculator

Use the calculator above for all basic and advanced mathematical operations.

Quick Examples

Theme:

Enhanced Matrix Operations

Perform advanced matrix operations with customizable dimensions up to 10×10!

Matrix A

Rows: Cols:

Matrix B

Rows: Cols:

Result:

Select an operation to see the result.

Matrix Examples

Advanced Probability & Combinatorics

Calculate probabilities, combinations, and statistical distributions!

Basic Probability

Combinations & Permutations

Normal Distribution

Binomial Distribution

Poisson Distribution

Hypergeometric Distribution

Probability Examples

Area & Volume Calculator

Calculate areas, perimeters, volumes, and surface areas with automatic unit conversion!

Unit:

2D Shapes

3D Shapes

Results will appear here

Area Examples

Advanced Statistical Analysis

Perform comprehensive statistical analysis including correlation, regression, and hypothesis testing!

Descriptive Statistics

Correlation & Regression Analysis

Hypothesis Testing

Confidence Intervals

ANOVA (Analysis of Variance)

Statistics Examples

Calculus Operations

Solve calculus problems with advanced mathematical functions!

Function Examples:

Try these calculus examples on the main calculator:

Advanced Engineering Calculations

Professional engineering calculations for all engineering disciplines!

Electrical Engineering

Mechanical Engineering

Civil Engineering

Chemical Engineering

Aerospace Engineering

Engineering Examples

Advanced Physics Calculations

Comprehensive physics calculations for all areas of physics!

Classical Mechanics

Thermodynamics

Electromagnetism

Quantum Physics

Relativity

Physics Examples

Advanced Financial & Commerce Calculations

Professional financial calculations for business, commerce, and personal finance!

Compound Interest & Investment

Loan & Mortgage Calculations

Business Finance & ROI

Break-Even Analysis

BCOM/Commerce Calculations

Depreciation Calculations

Finance Examples

Mathematical Equations Reference

Complete reference of all equations used in this calculator, organized by section!

Basic Calculator Equations

Basic Arithmetic: a + b, a - b, a × b, a ÷ b

Fundamental mathematical operations

Exponentiation: a^b = a × a × ... × a (b times)

Power operations

Square Root: √a = b where b² = a

Find number that when squared equals original value

Factorial: n! = n × (n-1) × (n-2) × ... × 1

Product of all positive integers from 1 to n

Trigonometric: sin(θ), cos(θ), tan(θ) = sin(θ)/cos(θ)

Basic trigonometric functions

Logarithms: log₁₀(x), ln(x) = logₑ(x)

Common and natural logarithms

Matrix Operations Equations

Matrix Addition: (A + B)ᵢⱼ = Aᵢⱼ + Bᵢⱼ

Add corresponding elements

Matrix Multiplication: (AB)ᵢⱼ = Σₖ Aᵢₖ × Bₖⱼ

Row-by-column multiplication

Determinant (2×2): det(A) = ad - bc

For matrix [[a,b],[c,d]]

Matrix Inverse: A⁻¹ = (1/det(A)) × adj(A)

Inverse using adjugate matrix

Transpose: (Aᵀ)ᵢⱼ = Aⱼᵢ

Flip matrix along diagonal

Trace: tr(A) = Σᵢ Aᵢᵢ

Sum of diagonal elements

Probability & Statistics Equations

Basic Probability: P(A) = Favorable outcomes / Total outcomes

Fundamental probability definition

Combinations: C(n,r) = n! / (r!(n-r)!)

Number of ways to choose r items from n

Permutations: P(n,r) = n! / (n-r)!

Number of ways to arrange r items from n

Normal Distribution: f(x) = (1/σ√(2π)) × e^(-½((x-μ)/σ)²)

Bell curve probability density function

Binomial Distribution: P(X=k) = C(n,k) × p^k × (1-p)^(n-k)

Probability of k successes in n trials

Mean: μ = Σxᵢ / n

Average value of dataset

Standard Deviation: σ = √(Σ(xᵢ - μ)² / n)

Measure of data spread

Correlation Coefficient: r = Σ((xᵢ-x̄)(yᵢ-ȳ)) / √(Σ(xᵢ-x̄)² × Σ(yᵢ-ȳ)²)

Measure of linear relationship

Area & Volume Equations

Square: Area = s², Perimeter = 4s

Where s is side length

Rectangle: Area = l × w, Perimeter = 2(l + w)

Where l is length, w is width

Circle: Area = πr², Circumference = 2πr

Where r is radius

Triangle: Area = ½ × base × height

For any triangle

Sphere: Volume = (4/3)πr³, Surface Area = 4πr²

Where r is radius

Cylinder: Volume = πr²h, Surface Area = 2πr(r + h)

Where r is radius, h is height

Engineering Equations

Ohm's Law: V = IR

Voltage = Current × Resistance

Electrical Power: P = VI = I²R = V²/R

Power in electrical circuits

Stress: σ = F/A

Force per unit area

Strain: ε = ΔL/L₀

Change in length per original length

Young's Modulus: E = σ/ε

Measure of material stiffness

Reynolds Number: Re = ρVD/μ

Dimensionless flow parameter

Beam Deflection: δ = (5wL⁴)/(384EI)

Maximum deflection for uniformly loaded beam

Physics Equations

Newton's Second Law: F = ma

Force equals mass times acceleration

Kinetic Energy: KE = ½mv²

Energy due to motion

Potential Energy: PE = mgh

Energy due to position

Momentum: p = mv

Mass times velocity

Coulomb's Law: F = k(q₁q₂)/r²

Electric force between charges

Einstein's Mass-Energy: E = mc²

Mass-energy equivalence

Photon Energy: E = hf

Energy of electromagnetic radiation

Wave Equation: v = fλ

Wave speed equals frequency times wavelength

Finance Equations

Simple Interest: SI = PRT

Principal × Rate × Time

Compound Interest: A = P(1 + r/n)^(nt)

Future value with compounding

Present Value: PV = FV / (1 + r)^n

Current value of future money

Monthly Payment: PMT = P[r(1+r)^n]/[(1+r)^n - 1]

Loan payment calculation

ROI: ROI = (Gain - Cost) / Cost × 100%

Return on investment percentage

NPV: NPV = Σ[CFₜ/(1+r)^t] - Initial Investment

Net present value of cash flows

Break-Even Point: Fixed Costs / (Price - Variable Cost)

Units needed to cover costs

Profit Margin: (Revenue - Costs) / Revenue × 100%

Percentage of revenue that is profit