GATE Agricultural Engineering (AG) Calculators
Calculators for the numerical questions in GATE Agricultural Engineering: farm machinery and power, soil and water conservation, irrigation and drainage, and agricultural process, dairy and food engineering.
40 calculators · 5 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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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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- 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.
- Binomial Distribution Calculator – Trials n, probability p and successes k → exact, cumulative and tail probabilities, mean and variance.
- Correlation & Regression Calculator – Paste x and y values → correlation r, R², slope, intercept and regression equation.
Farm Machinery
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Field Capacity Calculator
TFC = W S / 10, EFC = TFC × field efficiency
W in m, S in km/h, capacities in ha/h
Example: A 2.5 m implement at 5 km/h with 80 % field efficiency: Effective field capacity = 1 ha/h.
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Drawbar Power Calculator
DBP = Draft × Speed
Draft = specific draft × width × depth; kW = kN × m/s
Example: A plough cutting 90 cm × 15 cm in soil of 7 N/cm² specific draft at 4.5 km/h: Drawbar power = 11.8125 kW.
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- Seed Rate Calculator – Spacing, seeds per hill, test weight, germination and purity → kg/ha.
- Fertilizer Requirement Calculator – NPK recommendation (kg/ha) → urea, DAP or SSP and MOP needed.
- Farm Machinery Cost Calculator – Price, life, use, fuel and wages → fixed, variable and total cost per hour.
- Gear Train Calculator – Input speed and teeth on each meshing pair → speed ratio, output speed, direction and torque.
- Belt Tension Calculator – Maximum tension, belt mass, speed, μ and wrap angle → T₁, T₂, centrifugal tension and power.
Farm Power
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IC Engine Performance Calculator
BP = 2πNT / 60,000 kW
BSFC = ṁ_f/BP; η_bth = BP/(ṁ_f × CV); η_mech = BP/IP
Example: A diesel engine giving 200 N·m at 2000 rpm on 9 kg/h of 42 MJ/kg fuel: Brake power BP = 41.8879 kW.
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Wheel Slip Calculator
Slip = (1 − V_a/V_t) × 100
tractive efficiency = drawbar power / axle power
Example: A tractor with a no-slip speed of 6 km/h moving at 5.1 km/h: Wheel slip = 15 %.
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- Otto Cycle Calculator – Compression ratio, γ, intake state and peak temperature → efficiency, temperatures, work and MEP.
- Air–Fuel Ratio Calculator – Fuel formula and excess air → stoichiometric and actual air–fuel ratio, φ and λ.
Soil and Water Conservation Engineering
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USLE Soil Loss Calculator
A = R K LS C P
LS = (λ/22.13)^m (65.41 sin²θ + 4.56 sin θ + 0.065)
Example: R = 800, K = 0.03, LS = 1.2, C = 0.3 and P = 0.5: Average annual soil loss A = 4.32 t/(ha·yr).
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SCS Curve Number Calculator
Q = (P − Ia)² / (P − Ia + S)
S = 25,400/CN − 254 mm; Ia = λS (λ = 0.2)
Example: 100 mm of rain on a catchment with CN = 75: Direct runoff Q = 41.1371 mm.
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- Infiltration Calculator – Model parameters and time → infiltration rate and cumulative depth.
- Rational Method Calculator – Runoff coefficient, rainfall intensity and area → peak discharge.
- Manning's Equation Calculator – Channel shape, depth, slope and roughness → discharge, velocity and flow regime.
- 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.
Irrigation and Drainage Engineering
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Irrigation Requirement Calculator
d_net = (FC − PWP) ρb D × MAD
d_gross = d_net/η; interval = d_net/ETc; ETc = Kc ET₀
Example: A loam (FC 28 %, PWP 14 %, ρb 1.4) with a 0.6 m root zone, 50 % depletion and ETc 5.5 mm/day: Net irrigation depth = 58.8 mm.
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Evapotranspiration Calculator
ET₀ = p (0.46 T + 8.13)
Hargreaves: ET₀ = 0.0023 Ra (T_mean + 17.8)√(Tmax − Tmin); ETc = Kc ET₀
Example: A month with a mean temperature of 25 °C and p = 0.27: Reference evapotranspiration ET₀ = 5.3001 mm/day.
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- Sprinkler Irrigation Calculator – Discharge and spacing → application rate; catch-can depths → CU and DU.
- Drain Spacing Calculator – K, water-table height, equivalent depth and drainage coefficient → drain spacing.
- Pump Power Calculator – Discharge, head and efficiency → water and shaft power, and specific speed.
- Well Yield Calculator – Conductivity, aquifer thickness and heads at two radii → steady pumping rate.
Agricultural Process Engineering
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Grain Moisture Content Calculator
M_db = M_wb / (1 − M_wb)
final mass = initial mass × (1 − M_i)/(1 − M_f)
Example: 1000 kg of grain dried from 20 % to 12 % wet basis: Water to be removed = 90.9091 kg.
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Psychrometric Calculator
W = 0.622 p_v / (P − p_v)
h = 1.006T + W(2501 + 1.86T) kJ/kg dry air; p_v = RH × p_ws
Example: Air at 30 °C and 60 % relative humidity at sea level: Humidity ratio W = 16.0046 g/kg dry air.
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- Size Reduction Energy Calculator – Feed and product sizes with a work index or known energy → kWh/t and power.
- Specific Heat Calculator – Mass, specific heat and temperature change → heat energy; or any of the others.
- Centrifuge RCF Calculator – Rotor radius and rpm ↔ relative centrifugal force (× g).
Dairy and Food Engineering
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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.
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LMTD Calculator
LMTD = (ΔT₁ − ΔT₂) ÷ ln(ΔT₁/ΔT₂)
counter-flow ΔT₁ = Th,i − Tc,o, ΔT₂ = Th,o − Tc,i
Example: Counter-flow: hot 150 → 100 °C, cold 30 → 70 °C, Q = 200 kW, U = 500 W/m²·K: LMTD = 74.8888 °C.
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- Lumped Capacitance Calculator – Body size, h and properties → Biot number, time constant, and time to a temperature or temperature after a time.
- Sterilization Time Calculator – Spore load, acceptable survivors, temperature and D/z (or A, Eₐ) → holding time and Del factor.
Unit Converters for GATE Agricultural (AG)
- Application Rate Converter (kg/ha, lb/acre) – kg/ha, lb/acre, q/ha, t/ha
- Discharge Converter (Cumecs, Cusecs, MLD) – cumecs, cusecs, MLD, MGD, L/s
- Hydraulic Conductivity Converter (cm/s, m/day) – cm/s, m/day, ft/day, mm/h, gpd/ft²
- Area Converter – m², cm², mm², ft², in², test areas
- Power Converter – W, kW, MW, hp, PS, BTU/h, TR, kcal/h
Common GATE Agricultural (AG) Conversions
How to use these GATE Agricultural Engineering calculators
GATE Agricultural Engineering spans machines, water and processing. This hub has calculators for theoretical and effective field capacity, drawbar power from specific draft, wheel slip and tractive efficiency, IC engine brake power and specific fuel consumption, machinery operating cost, fertiliser quantities from an NPK recommendation, seed rate, irrigation depth and interval, sprinkler application rate and uniformity, Hooghoudt drain spacing, Blaney–Criddle and Hargreaves evapotranspiration, the USLE, the SCS curve number method, Horton and Kostiakov infiltration, grain moisture on wet and dry basis, psychrometry and pump power.
The inputs follow the units used in Indian agricultural engineering texts: hectares, km/h, N/cm² for specific draft, mm/day for evapotranspiration and drainage coefficients, and kg/ha for inputs. Shared tools for engineering mathematics, hydraulics, heat transfer and sterilisation are listed under their syllabus sections.
Use the application rate, discharge and hydraulic conductivity converters on this page for the conversions that appear inside these problems, such as lb/acre to kg/ha, cusecs to cumecs and cm/h to m/day.