GATE Electrical Engineering (EE) Calculators
Calculators for the numerical questions in GATE Electrical Engineering, grouped by syllabus section, each with units on every input and the working shown.
50 calculators · 8 converters · common conversions
Engineering Mathematics
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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 = LU, uᵢⱼ = aᵢⱼ − Σ lᵢₖuₖⱼ, lⱼᵢ = (aⱼᵢ − Σ lⱼₖuₖᵢ)/uᵢᵢ
Doolittle: L has 1s on the diagonal
Example: The matrix [[2, −1, −2], [−4, 6, 3], [−4, −2, 8]]: det A = product of U’s diagonal = 24.
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- Newton-Raphson Method Calculator – f(x), optional f′(x) and a starting guess → root, iteration table and convergence check.
- Numerical Integration Calculator – f(x), limits and intervals → trapezoidal, Simpson 1/3 and 3/8 results with a reference value.
- Euler Method Calculator – An ODE, initial value, step and end point → y by Euler, Heun, RK2 or RK4 with every step.
- Normal Distribution Calculator – Mean, standard deviation and bounds → normal probabilities, z-scores, density and percentiles.
- Bayes’ Theorem Calculator – Priors and likelihoods → total probability and posterior probabilities, with a Bayes table.
- Complex Number Calculator – Two complex numbers and an operation → result, modulus, argument and conjugate.
Electric Circuits
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Ohm's Law Calculator
V = I R, P = V I
V voltage, I current, R resistance, P power
Example: 12 V across 4 Ω drives 3 A and dissipates 36 W.
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Series and Parallel Calculator
R_s = R₁ + R₂ + …, 1/R_p = 1/R₁ + 1/R₂ + …
inductors combine like resistors; capacitors the other way round (parallel adds)
Example: Resistors of 100 Ω, 220 Ω and 470 Ω: Series equivalent = 790.
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- Voltage Divider Calculator – Input voltage and two resistors → output voltage, with load; or a current divider.
- Star-Delta Conversion Calculator – Three delta resistances → equivalent star, or star → delta.
- Maximum Power Transfer Calculator – Thevenin voltage and resistance → maximum load power, and power and efficiency at any load.
- RC & RL Time Constant Calculator – R and C (or L) → time constant and the voltage or current at any time t.
- RLC Resonance Calculator – R, L and C → resonant frequency, Q, bandwidth, half-power points and damping.
- Impedance Calculator – R, L, C and frequency → impedance magnitude, rectangular form, phase and power factor.
- Inductive Reactance Calculator – Frequency and inductance → inductive reactance; or solve for L or f.
- Capacitive Reactance Calculator – Frequency and capacitance → capacitive reactance; or solve for C or f.
- AC Power Calculator – Voltage, current and power factor → kW, kVA, kVAR and complex power.
- Power Factor Correction Calculator – Real power, present and target power factor → capacitor kVAR and µF per phase.
Electromagnetic Fields
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Coulomb's Law Calculator
F = k |q₁ q₂| / r²
k = 1/(4πε₀) = 8.9875517923 × 10⁹ N·m²/C², q the charges, r the distance between them
Example: Two +1 µC charges 10 cm apart in vacuum: Electrostatic force F = 0.898755 N.
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Electric Field Calculator
E = q/(4πε r²), λ/(2πε r), σ/(2ε)
ε = ε₀εᵣ; potential of a point charge V = q/(4πε r)
Example: A 1 nC point charge, 1 m away, in air: Electric field |E| = 8.98755 V/m.
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- Capacitance Calculator – Geometry and dielectric → capacitance in pF, nF and µF.
- Magnetic Field Calculator – Current and geometry → magnetic flux density B and field strength H.
- Inductance Calculator – Coil geometry, turns and core → inductance in µH, mH and H.
- Lorentz Force Calculator – Charge, speed and field (or current and length) → magnetic force, orbit radius and frequency.
Signals and Systems
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RMS Value Calculator
V_rms = √((1/T)∫v² dt)
sine V_p/√2, square V_p, triangle V_p/√3, half-wave V_p/2, pulse V_p√D
Example: A sine wave with a 325 V peak (230 V mains): RMS value = 229.81.
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Sampling Theorem Calculator
fₛ ≥ 2f_max
alias frequency f_a = |f − k fₛ| with k the nearest integer to f/fₛ
Example: A 4 kHz signal sampled at 6 kHz, and a 5 kHz tone in the same system: Nyquist rate 2f_max = 8 kHz.
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- DFT Calculator – A sequence x[n] → its DFT X[k] with magnitude and phase for each k.
- Convolution Calculator – Two sequences → their linear or circular convolution, sample by sample.
Electrical Machines
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Transformer Calculator
η = xS cos φ / (xS cos φ + Pᵢ + x²P_cu)
x load fraction, Pᵢ core loss, P_cu full-load copper loss; maximum η at x = √(Pᵢ/P_cu)
Example: A 100 kVA, 11 kV/415 V transformer with 500 W core loss and 1500 W full-load copper loss, at 75 % load and 0.8 power factor: Efficiency η = 97.8095 %.
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Induction Motor Slip Calculator
Nₛ = 120f/P, s = (Nₛ − N)/Nₛ
rotor frequency sf; rotor copper loss = sP_ag; mechanical power = (1 − s)P_ag
Example: A 4-pole, 50 Hz motor running at 1440 rpm with 10 kW crossing the air gap: Slip s = 4 %.
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DC Machine EMF Calculator
E = PΦZN / (60A)
A = P for lap, 2 for wave windings; motor: E_b = V − IₐRₐ, T = E_b Iₐ/ω
Example: A 4-pole lap-wound machine with 20 mWb per pole and 500 conductors at 1200 rpm: Generated EMF E = 200 V.
Power Systems
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Per-Unit Calculator
Z_new = Z_old (kV_old/kV_new)² (MVA_new/MVA_old)
Z_base = kV²/MVA; I_base = MVA/(√3 kV); fault MVA = MVA_base/Z_pu
Example: A 0.1 pu reactance on 50 MVA, 11 kV, moved to a 100 MVA, 11 kV base: Impedance on the new base = 0.2 pu.
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Symmetrical Components Calculator
V₁ = (V_a + aV_b + a²V_c)/3
V₀ = (V_a + V_b + V_c)/3, V₂ = (V_a + a²V_b + aV_c)/3, a = 1∠120°
Example: Unbalanced phases V_a = 100∠0°, V_b = 80∠−120°, V_c = 90∠120°: Positive sequence V₁ = 90 ∠ 0°.
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Wire Resistance Calculator
R = ρ L ÷ A
ρ resistivity, L conductor length, A cross-sectional area
Example: 100 m of 2.5 mm² copper = 0.69 Ω at 20 °C.
Control Systems
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Second-Order System Calculator
Mₚ = e^(−ζπ/√(1−ζ²)), tₚ = π/ω_d
ω_d = ωₙ√(1 − ζ²), t_r = (π − arccos ζ)/ω_d, t_s ≈ 4/(ζωₙ) (2 %)
Example: A system with ζ = 0.5 and ωₙ = 4 rad/s (s² + 4s + 16): Peak overshoot Mₚ = 16.3034 %.
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Routh-Hurwitz Calculator
bᵢ = (a₁a₂ᵢ − a₀a₂ᵢ₊₁)/a₁
number of sign changes in the first column = number of roots in the right half-plane
Example: The characteristic equation s⁴ + 2s³ + 3s² + 4s + 5 = 0: Result: Unstable: 2 roots in the right half-plane.
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Steady-State Error Calculator
e_ss = A/(1 + Kₚ), A/K_v, A/Kₐ
Kₚ = lim G(s), K_v = lim sG(s), Kₐ = lim s²G(s) as s → 0
Example: G(s) = 10 / [s(s + 1)(s + 5)] with a unit ramp input: Steady-state error (ramp) e_ss = 0.5.
Electrical and Electronic Measurements
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Wheatstone Bridge Calculator
Rₓ = R₂R₃ / R₁ at balance
Vₒᵤₜ = V_s [R₂/(R₁ + R₂) − Rₓ/(R₃ + Rₓ)]
Example: A bridge with equal 1 kΩ ratio arms balanced with R₃ = 470 Ω: Unknown resistance Rₓ = 470 Ω.
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Ammeter Shunt Calculator
R_sh = I_m R_m / (I − I_m), R_s = V/I_m − R_m
multiplying power m = I/I_m, so R_sh = R_m/(m − 1)
Example: A 1 mA, 100 Ω meter extended to read 1 A: Shunt resistance R_sh = 0.1001 Ω.
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Error Propagation Calculator
Sums: ΔA + ΔB; products: ΔA/A + ΔB/B
powers: Δy/y = |n| ΔA/A; statistical errors combine as √(Σ squares)
Example: A = 100 ± 1 and B = 20 ± 0.4 multiplied, limiting errors: Result y = 2000 ± 60.
Analog and Digital Electronics
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Op-Amp Gain Calculator
Inverting −R_f/Rᵢₙ, non-inverting 1 + R_f/Rᵢₙ
difference (R_f/Rᵢₙ)(V₂ − V₁); in-amp 1 + 2R/R_G; summing −(R_f/Rᵢₙ)ΣV
Example: An inverting amplifier with Rᵢₙ = 10 kΩ, R_f = 100 kΩ and 0.2 V in: Voltage gain = -10.
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555 Timer Calculator
f = 1/(ln 2 (R₁ + 2R₂)C) ≈ 1.44/((R₁ + 2R₂)C)
duty = (R₁ + R₂)/(R₁ + 2R₂); monostable T = ln 3 × RC ≈ 1.1RC
Example: An astable 555 with R₁ = 1 kΩ, R₂ = 10 kΩ and C = 10 µF: Frequency f = 6.86998 Hz.
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- ADC Resolution Calculator – Bits and reference voltage → LSB, the code for an input, quantisation error, SNR and ENOB.
- K-Map Solver – Minterms and don’t-cares → minimal sum of products, product of sums, prime and essential implicants.
- Number Base Converter – A number in any base 2–36 → binary, octal, decimal and hex, with fractional parts.
Power Electronics
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Rectifier Calculator
V_dc = 2Vₘ/π (no filter), V_r ≈ I/(f_r C)
f_r = f (half-wave) or 2f (full-wave); with a capacitor V_dc ≈ Vₘ − V_r/2
Example: A bridge rectifier on 12 V RMS, 0.7 V diodes, 50 Hz, 0.5 A load and 2200 µF: DC output voltage = 14.4342 V.
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Controlled Rectifier Calculator
V_dc = (2Vₘ/π) cos α (1-φ full), 1.35 V_LL cos α (3-φ full)
semi-converter (Vₘ/π)(1 + cos α); half-wave R load (Vₘ/2π)(1 + cos α)
Example: A single-phase full converter on 230 V with α = 30° and continuous current: Average output voltage V_dc = 179.33 V.
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DC-DC Converter Calculator
Buck Vₒ = DVᵢₙ, boost Vₒ = Vᵢₙ/(1 − D), buck-boost |Vₒ| = DVᵢₙ/(1 − D)
buck ripple ΔI = Vₒ(1 − D)/(fL), ΔV = ΔI/(8fC)
Example: A buck converter from 24 V at 50 % duty, 2 A load, 100 kHz, 100 µH, 100 µF: Output voltage Vₒ = 12 V.
Unit Converters for GATE Electrical (EE)
- Power Converter – W, kW, MW, hp, PS, BTU/h, TR, kcal/h
- Energy Converter – J, kJ, kWh, kcal, cal, BTU, therm, eV
- Frequency & RPM Converter – Hz, kHz, MHz, GHz, rpm, rad/s
- Electrical Resistivity Converter – Ω·m, Ω·cm, µΩ·cm, Ω·mm²/m, MΩ·cm
- Electrical Conductivity Converter – S/m, MS/m, µS/cm, mS/cm, dS/m, %IACS
- Magnetic Flux Density Converter – T, mT, µT, nT, G, mG, kG
- Magnetic Field Strength Converter – A/m, kA/m, A/cm, Oe, kOe
- Magnetic Flux Converter – Wb, mWb, µWb, Mx
Common GATE Electrical (EE) Conversions
- kilowatt to horsepower
- horsepower to kilowatt
- kilowatt-hour to BTU
- BTU to kilowatt-hour
- revolution per minute to hertz
- hertz to revolution per minute
- microohm centimetre to ohm metre
- ohm metre to microohm centimetre
- microsiemens per centimetre to millisiemens per centimetre
- millisiemens per centimetre to microsiemens per centimetre
- gauss to tesla
- tesla to gauss
How to use these GATE Electrical Engineering calculators
GATE EE rewards fast, exact arithmetic with complex numbers, per-unit quantities and transfer functions. These calculators cover the numerical core of each section: RLC transients and resonance, impedance and AC power, power factor correction, transformer efficiency, induction-motor slip, DC machine EMF, per-unit base changes, symmetrical components, Routh arrays, second-order time response, steady-state error and the standard power-electronic converters.
Every input takes the unit you have (mH or µF, kV or V, kHz or MHz) and is converted to SI before the formula runs, and each answer shows the substituted formula, so you can see where a factor of √3, 2π or 1000 entered. Where textbooks use different conventions, such as line or phase quantities in three-phase circuits, the input label says which one is expected.
Work the question on paper, then enter the same numbers to check. If the answers differ, compare the intermediate steps: the commonest slips are radians versus degrees, peak versus RMS values, and forgetting to change per-unit impedances to a common base.