Scientific Calculator
DEG | High Precision
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Calculation History
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
Enhanced Matrix Operations
Perform advanced matrix operations with customizable dimensions up to 10×10!
Matrix A
Matrix B
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!
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
Compute the numerical derivative and definite integral of a function f(x).
Function f(x)
Use x as the variable. Supported: + − × ÷ ^, sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, sqrt, cbrt, exp, ln, log, abs, pi, e. (Angles in radians.)
Derivative at a Point
Definite Integral
Calculus Examples
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