GATE Chemical Engineering (CH) Calculators
Calculators for the numerical questions in GATE Chemical Engineering: thermodynamics and phase equilibria, fluid and particle mechanics, heat and mass transfer, reaction engineering, process control and plant economics.
45 calculators · 6 converters · common conversions
Engineering Mathematics
-
Eigenvalue Calculator
det(A − λI) = 0
Σλ = trace A, Πλ = det A
Example: The matrix [[4, 1], [2, 3]]: Eigenvalues: λ₁ = 5, λ₂ = 2.
-
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.
Show 4 more
- 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.
- Normal Distribution Calculator – Mean, standard deviation and bounds → normal probabilities, z-scores, density and percentiles.
- Correlation & Regression Calculator – Paste x and y values → correlation r, R², slope, intercept and regression equation.
Process Calculations and Thermodynamics
-
Raoult’s Law Calculator
P = x₁P₁ˢᵃᵗ + x₂P₂ˢᵃᵗ, y₁ = x₁P₁ˢᵃᵗ/P
dew point: 1/P = y₁/P₁ˢᵃᵗ + y₂/P₂ˢᵃᵗ; α = P₁ˢᵃᵗ/P₂ˢᵃᵗ
Example: A benzene–toluene liquid with 40 % benzene at 90 °C: Bubble-point pressure P = 86.96 kPa.
-
Antoine Equation Calculator
log₁₀ P = A − B/(C + T)
P in mmHg, T in °C for the built-in constants
Example: Water at 100 °C: Vapour pressure P = 760.086 mmHg.
Show 4 more
- Van der Waals Equation Calculator – Gas, moles, volume and temperature → van der Waals pressure and Z.
- Ideal Gas Law Calculator – Solve PV = nRT for P, V, n or T in any pressure, volume and temperature units.
- Gibbs Phase Rule Calculator – Number of components and phases → degrees of freedom.
- Gibbs Free Energy Calculator – ΔH, ΔS and temperature → ΔG, equilibrium constant and crossover temperature.
Fluid Mechanics and Mechanical Operations
-
Reynolds Number Calculator
Re = ρ v D ÷ μ = v D ÷ ν
ρ density, v velocity, D pipe diameter, μ dynamic viscosity, ν kinematic viscosity
Example: Pipe flow is laminar below Re ≈ 2300 and turbulent above about 4000.
-
Pipe Pressure Drop Calculator
ΔP = f (L ÷ D) (ρ v² ÷ 2)
f Darcy friction factor (64/Re laminar, Colebrook–White turbulent), L pipe length, D inside diameter, ρ density, v mean velocity
Example: Darcy–Weisbach with the Colebrook friction factor.
Show 7 more
- Bernoulli Equation Calculator – Pressure, velocity and elevation at 1, velocity and elevation at 2 → pressure at 2 and heads.
- Venturi Meter Calculator – Inlet and throat diameters, manometer reading or Δp and Cd → actual and theoretical discharge.
- Ergun Equation Calculator – Particle size, voidage, velocity and fluid properties → bed pressure drop.
- Minimum Fluidization Velocity Calculator – Particle size and densities, viscosity → U_mf and fluidized-bed ΔP.
- Stokes' Law Settling Calculator – Particle size and density, fluid density and viscosity → settling velocity and Reynolds number.
- Cyclone Separator Calculator – Cyclone geometry, inlet velocity and particle properties → cut size and collection efficiency.
- Size Reduction Energy Calculator – Feed and product sizes with a work index or known energy → kWh/t and power.
Heat Transfer
-
Heat Conduction Calculator
Q = ΔT / R, R = L/kA, ln(r₂/r₁)/2πkL
composite: R = 1/hᵢA + Σ L/kA + 1/hₒA
Example: A 200 mm wall (k = 0.8 W/m·K, 10 m²) with faces at 40 °C and 10 °C: Heat transfer rate Q = 1200 W.
-
Dittus–Boelter Calculator
Nu = 0.023 Re^0.8 Prⁿ
n = 0.4 when the fluid is heated, 0.3 when cooled; h = Nu k/D
Example: Water being heated at Re = 50,000 and Pr = 5 in a 25 mm tube: Heat transfer coefficient h = 6035.36 W/(m²·K).
Show 4 more
- LMTD Calculator – Inlet and outlet temperatures and flow arrangement → LMTD and heat exchanger area.
- NTU Effectiveness Calculator – UA, capacity rates and inlet temperatures → NTU, effectiveness, heat duty and outlet temperatures.
- Radiation Heat Transfer Calculator – Temperatures, emissivities and area → net radiation, emissive power and Wien peak wavelength.
- Evaporator Calculator – Feed, concentrations, temperatures and latent heats → steam, economy and area.
Mass Transfer
-
Fick’s Law Calculator
N_A = (D_AB P / RTz) ln[(P − p_A2)/(P − p_A1)]
equimolar: N_A = D_AB (p_A1 − p_A2)/(RTz)
Example: Water evaporating at 25 °C through 10 mm of still air (D = 0.26 cm²/s): Molar flux N_A = 0.00337961 mol/(m²·s).
-
Fenske Equation Calculator
N_min = ln[(x_D/(1 − x_D))((1 − x_B)/x_B)] / ln α
N_min includes the reboiler as a stage
Example: Separating to 95 % and 5 % with α = 2.5: Minimum number of stages N_min = 6.42687.
Show 2 more
- Minimum Reflux Ratio Calculator – α, feed and distillate compositions and q → minimum reflux ratio.
- Kremser Equation Calculator – Gas compositions, m and L/V → absorption factor and ideal stages.
Chemical Reaction Engineering
-
Arrhenius Equation Calculator
k = A e^(−Eₐ/RT)
ln(k₂/k₁) = (Eₐ/R)(1/T₁ − 1/T₂)
Example: A process with A = 10¹³ and Eₐ = 150 kJ/mol at 800 K: Rate constant k = 1607.67.
-
CSTR and PFR Reactor Calculator
PFR: C/C₀ = e^(−kτ); CSTR: C/C₀ = 1/(1 + kτ)
N CSTRs in series: C/C₀ = (1 + kτ/N)^(−N), τ total
Example: A first-order reaction with k = 0.3 per hour and 8 h detention: PFR outlet C/C₀ = 0.090718.
Show 4 more
- Residence Time Distribution Calculator – Tracer concentrations over time → t̄, σ² and tanks in series.
- Michaelis-Menten Calculator – Km, Vmax and [S] (and inhibitor) → reaction rate; or rate data → Km and Vmax.
- Monod Equation Calculator – μmax, Ks and substrate concentration → specific growth rate and doubling time.
- Thiele Modulus Calculator – Particle size, rate constant and effective diffusivity → Thiele modulus and effectiveness factor.
Instrumentation and Process Control
-
First-Order System Response Calculator
y(t) = K M (1 − e^(−t/τ))
G(s) = K/(τs + 1); 63.2 % at t = τ
Example: A process with K = 2 and τ = 3 after a step of 5, at t = 6: Response y(t) = 8.64665.
-
Ziegler–Nichols Tuning Calculator
PID: K_c = 0.6K_u, τ_I = P_u/2, τ_D = P_u/8
reaction curve: K_c = 1.2τ/(Kθ), τ_I = 2θ, τ_D = 0.5θ
Example: A loop with ultimate gain 4 and ultimate period 2 min: PID controller gain K_c = 2.4.
Show 2 more
- Second-Order System Calculator – Damping ratio and natural frequency → overshoot, peak time, rise time, settling time and poles.
- Routh-Hurwitz Calculator – Characteristic equation coefficients → Routh array, right-half-plane roots and stability verdict.
Plant Design and Economics
-
Depreciation Calculator
Straight line: d = (P − S)/n
declining balance f = 1 − (S/P)^(1/n); SYD d_k = (P − S)(n − k + 1)/[n(n + 1)/2]
Example: Equipment costing 1,00,000 with a 10,000 salvage value and a 10-year life, year 3: Depreciation in year 3 = 9000.
-
Payback Period Calculator
Payback = years until Σ cash flow = investment
discounted: use CFₙ/(1 + r)ⁿ
Example: A 1,00,000 investment returning 30,000 rising by 5,000 a year: Simple payback period = 2.875 years.
Show 2 more
- NPV Calculator – Discount rate, initial investment and cash flows → NPV, PV table, profitability index and payback.
- IRR Calculator – Initial investment and cash flows → IRR, NPV profile and payback period.
Unit Converters for GATE Chemical (CH)
- Mass Flow Rate Converter (kg/s, kg/h, t/h, lb/h) – kg/s, kg/h, TPH, TPD, lb/h
- Specific Heat Converter (kJ/kg·K, BTU/lb·°F) – kJ/(kg·K), BTU/(lb·°F), cal/(g·°C)
- Specific Enthalpy Converter (kJ/kg, BTU/lb, kcal/kg) – kJ/kg, BTU/lb, kcal/kg, MJ/kg
- Gurley to Air Permeance Converter (Bendtsen, Frazier) – Gurley s, µm/(Pa·s), Bendtsen, Frazier
- Dynamic Viscosity Converter – Pa·s, mPa·s, cP, P, lbf·s/ft²
- Heat Transfer Coefficient Converter – W/(m²·K), BTU/(h·ft²·°F), kcal/(h·m²·°C), U-value
Common GATE Chemical (CH) Conversions
- kilogram per hour to kilogram per second
- kilogram per second to kilogram per hour
- BTU per pound degree Fahrenheit to kilojoule per kilogram kelvin
- kilojoule per kilogram kelvin to BTU per pound degree Fahrenheit
- BTU per pound to kilojoule per kilogram
- kilojoule per kilogram to BTU per pound
- Gurley second to micrometre per pascal second
- micrometre per pascal second to Gurley second
- centipoise to pascal-second
- pascal-second to centipoise
- BTU per hour square foot degree Fahrenheit to watt per square metre kelvin
- watt per square metre kelvin to BTU per hour square foot degree Fahrenheit
How to use these GATE Chemical Engineering calculators
GATE Chemical Engineering questions are long chains of calculation, so a slip early on carries through. This hub covers the syllabus with calculators for Raoult’s law bubble and dew points, Antoine vapour pressures, the van der Waals equation, Fenske minimum stages, Underwood minimum reflux, the Kremser absorber equation, Fick’s law, single-effect evaporators, the Ergun equation, minimum fluidization velocity, size-reduction laws, Dittus–Boelter heat transfer, Ziegler–Nichols tuning, first-order dynamics, depreciation, payback and residence time distributions, alongside the shared heat-exchanger, reactor and fluid-flow tools.
Each calculator states its assumptions, such as ideal solutions for Raoult’s law, constant relative volatility for Fenske and Underwood, and dilute solutions with straight lines for Kremser, so you can tell when a question needs a different model.
The mass flow rate, specific heat and specific enthalpy converters on this page handle the unit changes inside energy balances, such as kg/h to kg/s or kcal/kg to kJ/kg, and the air permeance converter covers Gurley seconds for membrane and paper problems.