GATE Engineering Mathematics Calculators
One calculator for each numerical method and formula in GATE Engineering Mathematics (XE-A and the maths section of every paper), with iteration tables and the full answer.
25 calculators · 1 converters · common conversions
Linear Algebra
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Matrix Rank Calculator
rank = number of non-zero rows in echelon form
unique if rank A = rank [A|b] = n; none if rank A < rank [A|b]
Example: The matrix [[1, 2, 3], [2, 4, 6], [1, 0, 1]]: Rank = 2.
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Eigenvalue Calculator
det(A − λI) = 0
Σλ = trace A, Πλ = det A
Example: The matrix [[4, 1], [2, 3]]: Eigenvalues: λ₁ = 5, λ₂ = 2.
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- LU Decomposition Calculator – A square matrix → lower and upper triangular factors L and U, and the determinant.
- Gauss Elimination Calculator – An augmented matrix → row operations, upper triangular system and the solution by back substitution.
- Matrix Calculator – A 2 × 2 or 3 × 3 matrix → determinant, inverse (as fractions), transpose and trace.
- Systems of Equations Calculator – Linear equations in two or three unknowns → exact solution, or a no / infinitely many solutions verdict.
Numerical Methods
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Newton-Raphson Method Calculator
xₙ₊₁ = xₙ − f(xₙ) ÷ f′(xₙ)
quadratic convergence near a simple root
Example: f(x) = x³ − 2x − 5 starting at x₀ = 2: Root x ≈ 2.09455148154.
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Bisection Method Calculator
c = (a + b)/2; regula falsi c = (a·f(b) − b·f(a)) ÷ (f(b) − f(a))
keep the half where f changes sign
Example: f(x) = x³ − x − 2 on [1, 2]: Root x ≈ 1.5213804245.
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- Secant Method Calculator – f(x) and two starting points → root by the secant method with each iteration.
- Lagrange Interpolation Calculator – Data points and x → interpolated value, Lagrange basis values and the polynomial.
- Newton Interpolation Calculator – Data points and x → divided-difference table, Newton polynomial and interpolated value.
- Numerical Differentiation Calculator – f(x), x and step h → forward, backward and central difference derivatives with their errors.
- Numerical Integration Calculator – f(x), limits and intervals → trapezoidal, Simpson 1/3 and 3/8 results with a reference value.
- Simpson’s Rule Calculator – Equally spaced ordinates and step h → integral by Simpson’s 1/3, 3/8 and trapezoidal rules.
- Euler Method Calculator – An ODE, initial value, step and end point → y by Euler, Heun, RK2 or RK4 with every step.
Probability and Statistics
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Bayes’ Theorem Calculator
P(A|B) = P(A)·P(B|A) ÷ P(B)
P(B) = Σ P(Hᵢ)·P(B|Hᵢ) (total probability)
Example: A disease with 1 % prevalence and a test with 95 % sensitivity and 5 % false positives: P(A | B) = 0.161016949153.
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Normal Distribution Calculator
z = (x − μ)/σ, P(X < x) = Φ(z)
Φ standard normal cumulative distribution
Example: X normal with μ = 50 and σ = 10, between 40 and 65: P(40 < X < 65) = 0.7745375448.
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- Binomial Distribution Calculator – Trials n, probability p and successes k → exact, cumulative and tail probabilities, mean and variance.
- Poisson Distribution Calculator – Mean rate λ and count k → exact, cumulative and tail Poisson probabilities.
- Exponential Distribution Calculator – Rate λ or mean and x → CDF, survival probability, density, mean, variance and median.
- Mean, Median and Mode Calculator – A list of numbers → mean, median, mode, range, quartiles and interquartile range.
- Standard Deviation Calculator – Paste a list of numbers → standard deviation, variance, mean, median, MAD and CV with steps.
- Correlation & Regression Calculator – Paste x and y values → correlation r, R², slope, intercept and regression equation.
Complex Variables
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Complex Number Calculator
(a + bi)(c + di) = (ac − bd) + (ad + bc)i
i² = −1; divide by multiplying by the conjugate
Example: (3 + 4i) × (1 − 2i): Result = 11 − 2i.
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De Moivre’s Theorem Calculator
[r(cos θ + i sin θ)]ⁿ = rⁿ(cos nθ + i sin nθ)
roots: r^(1/n)[cos((θ + 2πk)/n) + i sin((θ + 2πk)/n)]
Example: z = 1 + i with n = 3: zⁿ = z^3 = -2 + 2i.
Unit Converters for GATE Engineering Maths
- Angle Converter – degrees, radians, gradians, arcminutes
Common GATE Engineering Maths Conversions
How to use these GATE Engineering Mathematics calculators
Engineering Mathematics carries about 13 % of the marks in most GATE papers and is the compulsory XE-A section of the XE paper. The numerical part, linear algebra, numerical methods and probability, is where a calculator helps most, so each method here has its own tool that shows every iteration or row operation.
Type functions the way you write them, such as x^3 − 2x − 5 or xsin(x). Root-finding tools list each iteration, the integration tool compares the trapezoidal and Simpson rules with a high-accuracy reference value, and the ODE solver switches between Euler, modified Euler, RK2 and RK4 so you can see how the error shrinks with the method’s order.
GATE allows only the on-screen virtual calculator, so use these tools to practise and check previous-year questions, not to replace hand working. The iteration tables are laid out the way answer keys present them, so you can find the exact step where your own answer went wrong.