Math & Algebra Calculators

🧮 Addition Calculator — WebCalcSys Add multiple numbers with a dynamic input count. Choose from 2 to 10 values. Free online addition calculator.

🧮 Calculus Calculator — WebCalcSys Numerical integration using Simpson's rule and numerical differentiation using central difference. Free online calculus calculator.

🧮 Circumference Calculator — WebCalcSys Calculate circumference, area, diameter, and radius of a circle. Free online circle calculator.

🧮 Exponent & Root Calculator — WebCalcSys Calculate exponents, square roots, and cube roots. Free online exponent calculator.

🧮 Fraction Calculator — WebCalcSys Add, subtract, multiply, divide, and simplify fractions. Free online fraction calculator.

🧮 Geometry Calculator — WebCalcSys Calculate area, perimeter, surface area, and volume for common 2D and 3D shapes. Free online geometry calculator.

🧮 Linear Algebra Calculator — WebCalcSys Perform vector operations: addition, subtraction, dot product, cross product, magnitude, and angle between vectors. Free online linear algebra calculator.

🧮 Log Calculator — WebCalcSys Calculate logarithms with any base. Free online logarithm calculator.

🧮 Matrix Calculator — WebCalcSys Perform matrix operations: addition, subtraction, multiplication, determinant, transpose, and inverse for 2x2 and 3x3 matrices. Free online matrix calculator.

🧮 Number Base Converter — WebCalcSys Convert numbers between binary, octal, decimal, and hexadecimal. Free online base converter.

🧮 Prime Factor & Checker — WebCalcSys Check if a number is prime and find its prime factorization. Free online prime number tool.

🧮 Pythagorean Theorem Calculator — WebCalcSys Calculate the missing side of a right triangle using a² + b² = c². Free online Pythagorean theorem calculator.

🧮 Ratio & Proportion Calculator — WebCalcSys Simplify ratios, find missing values in proportions, and compare ratios. Free online ratio calculator.

🧮 Roman Numeral Converter — WebCalcSys Convert between Roman numerals and Arabic numbers. Free online Roman numeral converter.

🧮 Scientific Notation Calculator — WebCalcSys Convert between decimal and scientific notation. Free online scientific notation converter.

🧮 Significant Figures Calculator — WebCalcSys Count significant figures and round numbers. Free online sig fig calculator.

🧮 Slope Calculator — WebCalcSys Calculate the slope between two points. Free online slope calculator.

chaos theory Logistic Map x(n+1)=r*x(n)*(1-x(n))

universality Feigenbaum Constant Approximate Feigenbaum delta

fractal Mandelbrot Check Check if c is in Mandelbrot set

fractal Sierpinski Point Generate Sierpinski triangle point

chaos Bifurcation Point Bifurcation diagram y value

chaos Lorenz Attractor Step dx/dt = sigma(y-x)

∫ Simpson Integral ∫f(x)dx via Simpson rule

∫ Trapezoidal Integral ∫f(x)dx via trapezoid rule

√ Bisection Method Find root by bisection

sin Taylor Sin(x) sin(x) ≈ x - x³/3! + x⁵/5!

e^x Taylor e^x e^x ≈ 1 + x + x²/2! + x³/3!

∫ Riemann Sum ∫f(x)dx left Riemann sum

√ Secant Method x(n+1) = x(n) - f(x(n))(x(n)-x(n-1))/(f(x(n))-f(x(n-1)))

🔄 Fixed Point Iteration x = g(x)

📈 Lagrange Interpolation Interpolate points

Cₙ Catalan Number C(n) = (2n)!/((n+1)!n!)

Fₙ Nth Fibonacci F(n) = F(n-1) + F(n-2)

Lₙ Lucas Number L(n) = L(n-1) + L(n-2)

🔢 Collatz Steps Steps to reach 1

🔢 Goldbach Pairs p + q = n (both prime)

σ Sum of Divisors σ(n)

μ Möbius Function μ(n)

Bₙ Bernoulli Number B(n) B(n) via formula

Bₙ Bell Number Number of set partitions

📐 Pythagorean Triple a²+b²=c²

p(n) Integer Partitions p(n) number of partitions

🔢 Extended GCD ax+by = gcd(a,b)

🔢 Chinese Remainder x ≡ a (mod m)

🔢 Basic Calculator Perform basic arithmetic

% Percentage of Number X% of Y

📈 Percentage Change Increase/decrease %

➕ Addition Add numbers

➖ Subtraction Subtract numbers

✖️ Multiplication Multiply numbers

➗ Division Divide numbers

xʸ Power/Exponent x^y

x² Square x²

x³ Cube x³

√ Square Root √x

∛ Cube Root ∛x

√ⁿ Nth Root ⁿ√x

n! Factorial n! n!

|x| Absolute Value |x|

🔢 Rounding Round to precision

📊 Arithmetic Mean Average of numbers

🔗 Greatest Common Divisor GCD(a,b)

🔗 Least Common Multiple LCM(a,b)

% Modulo/Rest a mod b

🔢 Prime Number Check Is n prime?

🔬 Prime Factorization Break into primes

∑ Sum 1...n 1+2+...+n

∑ Sum of Squares 1²+...+n²

∑ Sum of Cubes 1³+...+n³

🔄 Reverse Digits 123→321

🔢 Sum of Digits 123→1+2+3=6

🔬 Scientific Notation → a×10^b

🎯 Significant Figures Round to n sig figs

¹/ₓ Reciprocal 1/x 1/x

🔢 Digital Root dr(n)

🔤 Number to Words 42→forty-two

📐 Linear Equation ax+b=0 Solve ax+b=0

📐 Linear Eq ax+b=cx+d Solve ax+b=cx+d

📐 System 2×2 Solve 2 equations

📐 Quadratic Formula ax²+bx+c=0

📈 Quadratic Vertex Parabola vertex y=ax²+bx+c

📐 Cubic t³+pt+q=0 Depressed cubic

📐 Linear Inequality ax+b>0

📐 Polynomial Evaluate Evaluate P(x)

📐 (a+b)² Expand (a+b)²

📐 (a+b)³ Expand (a+b)³

📊 Arithmetic Sequence nth term & sum

📊 Geometric Sequence nth term & sum

📊 Infinite Geometric Series Sum if |r|<1

📐 Partial Fractions Decompose 1/((x+a)(x+b))

📐 Synthetic Division Polynomial ÷ (x-c)

📐 Exponential Eq a^x=b Solve a^x=b

📐 Logarithmic Eq Solve log_a(x)=b

📐 Sum & Product of Roots Quadratic roots

📐 Complete Square x²+bx

🔢 Complex Add (a+bi)+(c+di)

🔢 Complex Multiply (a+bi)(c+di)

🔢 Complex Modulus |a+bi|

🔢 Complex→Polar r(cosθ+isinθ)

📐 Triangle Area (b,h) A=½bh

🔲 Rectangle Area & perimeter

▱ Parallelogram Area

⏢ Trapezoid Area Area

🔷 Rhombus Area & side

🪁 Kite Area A=½d₁d₂

⭕ Circle Area & circumference

🥧 Sector Area & arc length

🌙 Circle Segment Segment area

⭕ Annulus Ring area

🔵 Ellipse Area

⬡ Polygon Angles Interior angles

⬡ Regular Polygon Area Area of regular polygon

📐 Pythagorean Theorem a²+b²=c²

📏 2D Distance Distance between points

📍 Midpoint M=((x₁+x₂)/2,(y₁+y₂)/2)

📈 Slope Slope between points

📐 Circumcircle Circumradius of triangle

📐 Incircle Inradius of triangle

📍 Centroid Triangle centroid

📏 Point-Line Dist d=|Ax₀+By₀+C|/√(A²+B²)

📦 Cube V=s³, SA=6s²

📦 Rectangular Prism V=lwh

🔵 Sphere V=⁴⁄₃πr³

🥫 Cylinder V=πr²h

🍦 Cone V=⅓πr²h

🔺 Pyramid V=⅓×base×h

🍩 Torus Donut volume

📐 Frustum Conical frustum volume

🌓 Hemisphere Half sphere

⚽ Ellipsoid V=⁴⁄₃πabc

💊 Capsule Cylinder+hemispheres

🔺 Tetrahedron Regular tetrahedron

📐 Sin, Cos, Tan Basic trig functions

📐 arcsin, arccos, arctan Inverse trig

📐 csc, sec, cot Reciprocal trig

📐 Law of Sines a/sinA=b/sinB

📐 Law of Cosines c²=a²+b²-2ab·cosC

📐 sinh, cosh, tanh Hyperbolic functions

🔄 Radians↔Degrees Convert angle units

📐 sin²+cos²=1 Verify trig identity

📐 sin2θ, cos2θ Double angle

📐 sin(θ/2), cos(θ/2) Half angle

📐 sin(A±B), cos(A±B) Sum of angles formulas

📈 d/dx x^n Derivative of power

📈 Polynomial Derivative d/dx(ax³+bx²+cx+d)

📈 d/dx sin(x) Derivative of sine

📈 d/dx e^x Derivative of e^x

📊 ∫x^n dx Definite integral

📊 ∫sin(x)dx Integral of sine

📊 ∫cos(x)dx Integral of cosine

📊 ∫e^x dx Integral of e^x

📊 Trapezoidal Rule Numerical integration

📈 Limit f(x) Evaluate limit

📊 Median Middle value

📊 Mode Most frequent

📊 Std Deviation Population std dev

📊 Z-Score z=(x-μ)/σ

📈 Linear Regression Line of best fit

📊 Pearson r Correlation coefficient

📐 Permutation nPr nPr=n!/(n-r)!

📐 Combination nCr nCr=n!/[r!(n-r)!]

📊 Binomial Prob P(k) = C(n,k)p^k(1-p)^(n-k)

📊 Normal PDF Normal density

📊 Normal CDF Normal cumulative

📊 Poisson Prob P(k) = λ^k·e^(-λ)/k!

📊 Geometric Prob P(k) = (1-p)^(k-1)×p

📊 Expected Value E[X] Σx·P(x)

📐 Binomial Coeff C(n,k) Efficient C(n,k)

📊 Uniform PDF Uniform density f(x)=1/(b-a)

🔢 Fibonacci F(n) nth Fibonacci

🔢 Fibonacci Sequence Generate sequence

Φ Golden Ratio φ φ=(1+√5)/2

🔢 Catalan C(n) Cₙ=(2n)!/((n+1)!n!)

🔢 τ(n) Divisor Count Number of divisors

🔢 Perfect Number Is n perfect?

🔢 Collatz Sequence 3n+1 problem

📐 Pythagorean Triple m²-n², 2mn, m²+n²

📊 Log_b(x) Log any base

📊 Natural Log ln(x) ln(x)

📊 Log₁₀(x) Base 10 log

📊 Log₂(x) Base 2 log

📊 Sigmoid σ(x) σ(x)=1/(1+e⁻ˣ)

📊 ReLU(x) max(0,x)

📊 Gaussian f(x) ae^(-(x-b)²/(2c²))

📈 Exponential Growth P(t)=P₀e^(rt)

📈 Exponential Decay P(t)=P₀e^(-rt)

📈 Logistic Growth P(t)=K/(1+((K-P₀)/P₀)e^(-rt))

📐 Linear Interpolation y=y₁+(x-x₁)(y₂-y₁)/(x₂-x₁)

📐 Manhattan Distance L1 distance

📐 Chebyshev Distance L∞ distance

🌍 Haversine Dist Great-circle distance

🔢 Roman Numerals Number→Roman

🔢 Parse Roman Numerals Roman→Number

📊 Gamma Γ(n) Γ(n)=(n-1)!

📐 Quadratic Bezier B(t)=(1-t)²P₀+2(1-t)tP₁+t²P₂

📐 System of 2 Equations Solve a1x+b1y=c1, a2x+b2y=c2

📐 Quadratic Roots x = (-b +/- sqrt(b2-4ac))/(2a)

📐 Polynomial Evaluation Evaluate a0+a1x+a2x2+a3x3

🔢 Absolute Value |x| = x if x>=0 else -x

📐 Linear Interpolation y = y1+(x-x1)*(y2-y1)/(x2-x1)

📐 2D Distance sqrt((x2-x1)^2+(y2-y1)^2)

📐 Slope of Line m = (y2-y1)/(x2-x1)

📐 Perpendicular Slope m_perp = -1/m

⭕ Circle from Radius Area and circumference of circle

📐 Distance Point to Line |Ax0+By0+C|/sqrt(A^2+B^2)

🔢 Discriminant D = b^2-4ac

➡️ Vector Addition (a1+b1, a2+b2)

➡️ Dot Product A·B = a1*b1+a2*b2

➡️ 2D Cross Product AxB = a1*b2-a2*b1

➡️ Vector Magnitude |v| = sqrt(x^2+y^2)

➡️ Unit Vector u-hat = v/|v|

➡️ Vector Angle theta = atan2(y,x)

📐 Triangle Area A = 0.5*b*h

📐 Triangle Area (Heron) A = sqrt(s(s-a)(s-b)(s-c))

⭕ Circle Area A = pi*r^2

🌐 Sphere Volume V = (4/3)*pi*r^3

🧊 Cylinder Volume V = pi*r^2*h

📐 Cone Volume V = (1/3)*pi*r^2*h

🧊 Cube Volume V = s^3

📐 Pyramid Volume V = (1/3)*l*w*h

📐 Regular Polygon Area A = 0.5*n*R^2*sin(2*pi/n)

⭕ Torus Volume V = 2*pi^2*R*r^2

🧊 Cube Diagonal d = s*sqrt(3)

📐 Golden Ratio phi = (1+sqrt(5))/2

sin Sine sin(theta)

cos Cosine cos(theta)

tan Tangent tan(theta)

csc Cosecant csc(theta) = 1/sin(theta)

sec Secant sec(theta) = 1/cos(theta)

cot Cotangent cot(theta) = 1/tan(theta)

asin Arcsin theta = sin^-1(x)

acos Arccos theta = cos^-1(x)

atan Arctan theta = tan^-1(x)

atan2 Arctan2(y,x) theta = atan2(y,x)

sinh Hyperbolic Sine sinh(x) = (e^x-e^-x)/2

cosh Hyperbolic Cosine cosh(x) = (e^x+e^-x)/2

tanh Hyperbolic Tangent tanh(x) = sinh(x)/cosh(x)

📐 Law of Sines a/sin(A)=b/sin(B)=c/sin(C)

📐 Law of Cosines c^2=a^2+b^2-2ab*cos(C)

convert Degrees to Radians rad = deg*pi/180

sin2 Double Angle sin(2theta) sin(2theta) = 2sin(theta)cos(theta)

cos2 Double Angle cos(2theta) cos(2theta) = cos^2-sin^2

average Mean (Average) x-bar = sum(x)/n

median Median Middle value of sorted data

mode Mode Most frequent value

range Range max - min

variance Variance sigma^2 = sum(x-x-bar)^2/n

z Z-Score z = (x-mu)/sigma

quartile Quartiles Q1, Q2, Q3

covariance Covariance cov = sum(x-x-bar)(y-y-bar)/n

correlation Correlation r = cov/(sx*sy)

average Harmonic Mean n/(1/x1+1/x2+...)

average Geometric Mean (x1*x2*...)^(1/n)

rms RMS sqrt((x1^2+x2^2+...)/n)

skew Skewness g1 = (1/n)sum((x-x-bar)/sigma)^3

kurtosis Kurtosis g2 = (1/n)sum((x-x-bar)/sigma)^4-3

percentile Percentile P-th percentile of data

iqr Interquartile Range IQR = Q3-Q1

mad Mean Absolute Deviation MAD = (1/n)sum|x-x-bar|

chebyshev Chebyshev Inequality P(|x-mu|>=k*sigma) <= 1/k^2

stats Empirical Rule % within k*sigma (68-95-99.7)

sma Simple Moving Average SMA = sum(xi)/n

se Standard Error SE = sigma/sqrt(n)

me Margin of Error ME = z*sigma/sqrt(n)

sequence Infinite Geometric Sum S_inf = a/(1-r) for |r|<1

sum Telescoping Sum sum(1/k-1/(k+1)) = 1-1/(n+1)

sum p-Series Sum sum(1/k^p)

sum Alternating Series sum((-1)^(k+1)/k)

!! Double Factorial n!! n!! = n*(n-2)*(n-4)*...

fib Fibonacci Check Is n in Fibonacci sequence?

tri Triangular Number T_n = n(n+1)/2

sq Square Number S_n = n^2

pen Pentagonal Number P_n = n(3n-1)/2

hex Hexagonal Number H_n = n(2n-1)

fib Tribonacci T(n)=T(n-1)+T(n-2)+T(n-3)

binom Binomial Expansion (a+b)^n expansion

sigma Summation Calculator sum(f(k), k=a..b)

pi Product Calculator prod(f(k), k=a..b)

matrix Matrix Addition 2x2 A + B (2x2)

matrix Matrix Multiply 2x2 A x B (2x2)

matrix Determinant 2x2 det = ad-bc

matrix Inverse 2x2 A^-1 = (1/det)*[d,-b;-c,a]

convert Polar to Rect x = r*cos, y = r*sin

convert Rect to Polar r = sqrt(x^2+y^2), theta = atan2(y,x)

prob Probability Addition P(A or B)=P(A)+P(B)-P(A and B)

prob Conditional Probability P(A|B) = P(A and B)/P(B)

comb Combinations C(n,k) = n!/(k!(n-k)!)

perm Permutations P(n,k) = n!/(n-k)!

prob Bernoulli Trial P(k) = C(n,k)*p^k*(1-p)^(n-k)

prob Expected Value E[X] = sum(x*P(x))

📊 Binomial Distribution P(X=k) = C(n,k)*p^k*(1-p)^(n-k)

📊 Poisson Distribution P(X=k) = (lambda^k*e^-lambda)/k!

log Log Base 10 log10(x)

ln Natural Log ln(x)

exp Exponential e^x e^x

^ Power x^y x^y

√ Square Root sqrt(x)

∛ Cube Root cbrt(x)

🔢 GCD via Euclid gcd(a,b) by Euclidean algorithm

🔢 LCM lcm(a,b) = |a*b|/gcd(a,b)

🔢 Roman Numeral Converter Convert number to roman

🔢 Scientific Notation Convert to scientific notation

🔢 Significant Figures Count sig figs in number

🔢 Modulo a mod b

🎲 Random Number Generator Random number in range

🔢 Rounding Round to n decimal places

🔢 Floor Floor(x) = greatest int <= x

🔢 Ceiling Ceil(x) = smallest int >= x

🔢 Integer Part trunc(x) = integer part

📐 Hypotenuse c = sqrt(a^2+b^2)