Converts university Cumulative Grade Point Average (CGPA) on 10-point and 4-point scales into exact percentage marks under CBSE and UGC conversion rules.

CGPA / GPA ScoreGrading Scale (10.0 or 4.0)Multiplier (Default 9.5)

Percentage = CGPA × 9.5 (Indian 10-point) or (GPA / 4.0) × 100Launch

Descriptive Statistics№ 03.04

Standard Deviation & Variance Calculator

Computes population and sample standard deviation, variance, mean, and sum of squared deviations with full step-by-step arithmetic proofs.

Dataset {x₁, x₂, ..., xₙ}Population (N) vs Sample (n-1) Toggle

σ = √[Σ(x - μ)² / N] ; s = √[Σ(x - x̄)² / (n - 1)]Launch

Proportions & Percentages№ 03.05

Universal Unit Converter (Length, Weight, Temp)

Performs bidirectional metric and imperial conversions across length, weight, and temperature dimensions with high floating-point precision.

Category (Length, Mass, Temperature)Source UnitTarget UnitInput Value

y = x · factor ; °F = (°C · 9/5) + 32 ; K = °C + 273.15Launch

Algebra & Number Theory№ 03.06

LCM & HCF (GCD) Calculator with Step-by-Step Euclidean Algorithm

Determines the Least Common Multiple (LCM) and Highest Common Factor (HCF / GCD) of two or more integers via the Euclidean division algorithm.

Integer 1 (a)Integer 2 (b)Optional Integer 3 (c)

GCD(a,b) via a mod b ; LCM(a,b) = (|a · b|) / GCD(a,b)Launch

Algebra & Number Theory№ 03.07

Quadratic Equation Solver with Step-by-Step Formula

Solves quadratic polynomials ax² + bx + c = 0, determining the discriminant, vertex coordinates, and real or complex roots with algebraic steps.

Coefficient a (≠ 0)Coefficient bConstant c

x = [−b ± √(b² − 4ac)] / (2a) ; D = b² − 4acLaunch

Algebra & Number Theory№ 03.08

Permutation & Combination Calculator (nPr & nCr)

Computes permutations nPr (order matters) and combinations nCr (order does not matter) with full factorial factor expansions.

Total Items (n)Items Selected (r)

nPr = n! / (n − r)! ; nCr = n! / [r! · (n − r)!]Launch

Proportions & Percentages№ 03.09

Ratio Simplifier & Equivalent Proportions Calculator

Reduces ratios a : b to lowest fractional terms by dividing by their greatest common divisor and computes scaled equivalent proportions.

First Term (a)Second Term (b)Scaling Multiplier

Simplified = [a / GCD(a,b)] : [b / GCD(a,b)]Launch

Algebra & Number Theory№ 03.10

Prime Factorization & Factor Tree Calculator

Decomposes any positive integer into its canonical prime factor product with exponential powers, listing all divisors and primality verification.

Integer n (≥ 2)

n = p₁ᵃ¹ · p₂ᵃ² · ... · pₖᵃᵏ (Fundamental Theorem of Arithmetic)Launch

Algebra & Number Theory№ 03.11

Matrix Determinant Calculator (2×2 & 3×3)

Computes determinants for 2×2 and 3×3 square matrices with explicit Laplace cofactor expansions and geometric singularity checks.

Matrix Dimensions (2×2 or 3×3)Matrix Entries [a, b, c, d, ...]

det(2×2) = ad − bc ; det(3×3) = a(ei − fh) − b(di − fg) + c(dh − eg)Launch

Descriptive Statistics№ 03.12

Probability Calculator (Independent, Conditional & Unions)

Calculates classical event probabilities, independent intersections P(A ∩ B), unions P(A ∪ B), and complements P(A').

Favorable OutcomesTotal Sample SpaceProbability of Event AProbability of Event B

P(A) = n(E) / n(S) ; P(A ∪ B) = P(A) + P(B) − P(A ∩ B)Launch

Geometry№ 03.13

Area & Perimeter Geometry Calculator (All Shapes)

Computes geometric surface area and boundary perimeter for Rectangles, Circles, Triangles, Squares, Trapezoids, Parallelograms, and L-Shaped Rooms with material estimates.

Shape SelectorDimensions (Length, Width, Radius, Height, Sides)

Rect: A=l·w, P=2(l+w) ; Circle: A=πr², C=2πr ; Tri: A=½·b·h ; Square: A=s², P=4s ; L-Shape: A=L₁W₁-L₂W₂Launch

Explore Other Disciplines

Division 01

Finance & Investment

37 tools37 interactive computational models

Division 02

Health & Biophysics

20 tools20 interactive computational models

Division 04

Date & Time Chronology

11 tools11 interactive computational models

Division 05

Unit & Measurement Conversion

5 tools5 interactive computational models

Division 06

Home & Construction

4 tools4 interactive computational models

Division 07

Everyday & Productivity

3 tools3 interactive computational models

Verified Formulas & 100% Private Calculations

All Pure & Applied Mathematics calculators run 100% privately in your local browser. No calculation data is ever stored or shared. We use standard formulas and verified algorithms so you can trust your results every time.