Math & Algebra Calculators
Access free, interactive calculators for math & algebra. Click any tool to open the workspace on WebCalcSys.com.
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.
Logistic Map
x(n+1)=r*x(n)*(1-x(n))
Feigenbaum Constant
Approximate Feigenbaum delta
Mandelbrot Check
Check if c is in Mandelbrot set
Sierpinski Point
Generate Sierpinski triangle point
Bifurcation Point
Bifurcation diagram y value
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
Taylor Sin(x)
sin(x) ≈ x - x³/3! + x⁵/5!
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
Catalan Number
C(n) = (2n)!/((n+1)!n!)
Nth Fibonacci
F(n) = F(n-1) + F(n-2)
Lucas Number
L(n) = L(n-1) + L(n-2)
Collatz Steps
Steps to reach 1
Goldbach Pairs
p + q = n (both prime)
Sum of Divisors
σ(n)
Möbius Function
μ(n)
Bernoulli Number B(n)
B(n) via formula
Bell Number
Number of set partitions
Pythagorean Triple
a²+b²=c²
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
Power/Exponent
x^y
Square
x²
Cube
x³
Square Root
√x
Cube Root
∛x
Nth Root
ⁿ√x
Factorial n!
n!
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
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
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
Sine
sin(theta)
Cosine
cos(theta)
Tangent
tan(theta)
Cosecant
csc(theta) = 1/sin(theta)
Secant
sec(theta) = 1/cos(theta)
Cotangent
cot(theta) = 1/tan(theta)
Arcsin
theta = sin^-1(x)
Arccos
theta = cos^-1(x)
Arctan
theta = tan^-1(x)
Arctan2(y,x)
theta = atan2(y,x)
Hyperbolic Sine
sinh(x) = (e^x-e^-x)/2
Hyperbolic Cosine
cosh(x) = (e^x+e^-x)/2
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)
Degrees to Radians
rad = deg*pi/180
Double Angle sin(2theta)
sin(2theta) = 2sin(theta)cos(theta)
Double Angle cos(2theta)
cos(2theta) = cos^2-sin^2
Mean (Average)
x-bar = sum(x)/n
Median
Middle value of sorted data
Mode
Most frequent value
Range
max - min
Variance
sigma^2 = sum(x-x-bar)^2/n
Z-Score
z = (x-mu)/sigma
Quartiles
Q1, Q2, Q3
Covariance
cov = sum(x-x-bar)(y-y-bar)/n
Correlation
r = cov/(sx*sy)
Harmonic Mean
n/(1/x1+1/x2+...)
Geometric Mean
(x1*x2*...)^(1/n)
RMS
sqrt((x1^2+x2^2+...)/n)
Skewness
g1 = (1/n)sum((x-x-bar)/sigma)^3
Kurtosis
g2 = (1/n)sum((x-x-bar)/sigma)^4-3
Percentile
P-th percentile of data
Interquartile Range
IQR = Q3-Q1
Mean Absolute Deviation
MAD = (1/n)sum|x-x-bar|
Chebyshev Inequality
P(|x-mu|>=k*sigma) <= 1/k^2
Empirical Rule
% within k*sigma (68-95-99.7)
Simple Moving Average
SMA = sum(xi)/n
Standard Error
SE = sigma/sqrt(n)
Margin of Error
ME = z*sigma/sqrt(n)
Infinite Geometric Sum
S_inf = a/(1-r) for |r|<1
Telescoping Sum
sum(1/k-1/(k+1)) = 1-1/(n+1)
p-Series Sum
sum(1/k^p)
Alternating Series
sum((-1)^(k+1)/k)
Double Factorial n!!
n!! = n*(n-2)*(n-4)*...
Fibonacci Check
Is n in Fibonacci sequence?
Triangular Number
T_n = n(n+1)/2
Square Number
S_n = n^2
Pentagonal Number
P_n = n(3n-1)/2
Hexagonal Number
H_n = n(2n-1)
Tribonacci
T(n)=T(n-1)+T(n-2)+T(n-3)
Binomial Expansion
(a+b)^n expansion
Summation Calculator
sum(f(k), k=a..b)
Product Calculator
prod(f(k), k=a..b)
Matrix Addition 2x2
A + B (2x2)
Matrix Multiply 2x2
A x B (2x2)
Determinant 2x2
det = ad-bc
Inverse 2x2
A^-1 = (1/det)*[d,-b;-c,a]
Polar to Rect
x = r*cos, y = r*sin
Rect to Polar
r = sqrt(x^2+y^2), theta = atan2(y,x)
Probability Addition
P(A or B)=P(A)+P(B)-P(A and B)
Conditional Probability
P(A|B) = P(A and B)/P(B)
Combinations
C(n,k) = n!/(k!(n-k)!)
Permutations
P(n,k) = n!/(n-k)!
Bernoulli Trial
P(k) = C(n,k)*p^k*(1-p)^(n-k)
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 Base 10
log10(x)
Natural Log
ln(x)
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)
About Math & Algebra Calculations & Formulas
Welcome to the Math & Algebra Calculators directory. In both daily life and professional fields, performing calculations accurately is essential for making informed decisions. Our suite of calculators in the Math & Algebra category is designed to simplify complex math, formulas, and data analysis so you can get immediate, reliable results. Whether you are a student, professional, or hobbyist, these reference tools are here to help you calculate key metrics with ease.
This collection features interactive calculation tools such as Addition Calculator — WebCalcSys, Calculus Calculator — WebCalcSys, and Circumference Calculator — WebCalcSys. Each tool is built on verified mathematical models and formulas, translating raw inputs into clear, actionable outcomes. For example, Addition Calculator — WebCalcSys helps you add multiple numbers with a dynamic input count. choose from 2 to 10 values. free online addition calculator, while other tools in this category help with related measurements and conversions. By automating these steps, you can focus on analyzing the results rather than doing manual algebra or arithmetic.
Using these math & algebra calculators ensures accuracy, consistency, and speed. Instead of manually looking up formulas or risking calculation errors, you can run multiple scenarios, compare figures, and verify your results instantly. All calculators are free to use and cross-linked with the advanced interactive workspace on WebCalcSys.com for complete sheets, export functions, and graphs.
Browse Other Calculator Categories
Explore calculation sheets and guides in other mathematical and scientific fields.
Save Configuration Snapshot
Save current parameters to your dashboard for instant one-click reloading.
About This Calculator & Guide
About the Math, Fraction, Algebra & Standard Deviations Calculator
The Math, Fraction, Algebra & Standard Deviations Calculator is a specialized online utility designed to help you solve quadratic formulas, calculate standard deviation, count significant figures, and perform matrix operations. It performs calculations in real-time to provide immediate, reliable estimates for study, work, or daily tasks.
How to Use
Simply enter your parameters in the input fields of the calculator widget above. The tool evaluates the inputs instantly and displays the results in real-time. You can modify any value to check alternate scenarios and compare figures dynamically.
Data Privacy & Safety
All calculations are executed locally within your web browser. No inputs are sent to our servers or stored externally, ensuring your personal and financial details remain completely private and secure.
FAQ
Frequently Asked Questions
What does the Math, Fraction, Algebra & Standard Deviation Calculators do? +
Solve quadratic formulas, calculate standard deviation, count significant figures, and perform matrix operations. It is designed for quick everyday use and gives clear results without requiring a sign in.
Is the Math, Fraction, Algebra & Standard Deviation Calculators free to use? +
Yes. The Math, Fraction, Algebra & Standard Deviation Calculators is free to use online and works directly in your browser.
Can I use the Math, Fraction, Algebra & Standard Deviation Calculators on mobile? +
Yes. The calculator layout is responsive, so you can use it on phones, tablets, laptops, and desktop screens.