GATE Architecture and Planning (AR) Calculators
Calculators for the numerical questions in GATE Architecture and Planning: development controls and densities, building physics and services, circulation, infrastructure and real-estate valuation.
23 calculators · 4 converters · common conversions
Architecture, Planning and Design
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Floor Area Ratio Calculator
FAR = total built-up area / plot area
floors at full coverage = FAR / ground coverage
Example: A 1000 m² plot with FAR 2.5 and 40 % ground coverage: Maximum built-up area = 2500 m².
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Staircase Design Calculator
Risers = ⌈H / R_max⌉, 2R + T ≈ 600–640 mm
treads = risers − 1 per flight
Example: A 3 m floor height with risers up to 175 mm and 250 mm treads in a dog-legged stair: Number of risers = 18.
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- Ramp Slope Calculator – Rise with gradient → ramp length; or rise and length → gradient.
- Area Calculator – Pick a shape, enter its sides in any unit, and get the area in m², ft², acres or hectares with steps.
Construction and Management
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Critical Path (CPM) Calculator
Total float = LS − ES = LF − EF
ES = max EF of predecessors; LF = min LS of successors
Example: Six activities A–F with durations 3, 4, 2, 5, 3 and 2: Project duration = 14.
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PERT Calculator
tₑ = (a + 4m + b)/6, σ² = ((b − a)/6)²
z = (T − Σtₑ)/√Σσ² on the critical path
Example: Critical-path activities (2, 4, 6), (3, 5, 9) and (4, 6, 8) with a target of 17: Expected project duration Te = 15.3333.
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- Singly Reinforced Beam Calculator – b, d, fck, fy and Ast → neutral axis, section type and Mu.
- Beam Deflection Calculator – Cantilever or simply supported, point load or UDL → maximum deflection, slope, moment and shear.
Environmental Planning and Climate-Responsive Design
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Solar Angle Calculator
sin α = sin φ sin δ + cos φ cos δ cos h
δ = 23.45 sin(360(284 + n)/365); h = 15° × (t − 12)
Example: Latitude 23° N at solar noon on 21 June: Solar altitude α = 89.5502 °.
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U-Value Calculator
U = 1 / (R_si + Σ d/λ + R_so)
R_si = 0.13, R_so = 0.04 m²·K/W for walls (ISO 6946)
Example: A 230 mm brick wall plastered 20 mm on both faces: U-value = 1.96268 W/(m²·K).
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- Psychrometric Calculator – Dry-bulb temperature, RH and pressure → humidity ratio, dew point and enthalpy.
- Noise Level Calculator – Sound levels and times or distances → combined level, Leq, Ldn or level at a new distance.
Planning Process and Housing
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Residential Density Calculator
Density = dwelling units / area
gross uses the whole site; net only the residential plots
Example: 300 dwellings of 4.5 persons on a 2 ha site with 1.2 ha in plots: Gross density = 150 DU/ha.
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Population Forecast Calculator
Pₙ = P + n x̄ + n(n + 1)ȳ/2
arithmetic Pₙ = P + n x̄; geometric Pₙ = P(1 + r)ⁿ; x̄ average increase, ȳ average incremental increase
Example: Census figures 40,000, 46,000, 54,000, 64,000 and 77,000 over five decades, forecast two decades ahead: Incremental increase forecast (2 intervals) = 102500.
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- Years’ Purchase Calculator – Net income, interest and term → years’ purchase and capitalised value.
- Present Value Calculator – Future value, rate and periods → present value and discount factor.
Services and Infrastructure
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Water Demand Calculator
Q = P × q / 10⁶ MLD
peak factor 3.0 (< 50,000), 2.5 (to 2 lakh), 2.0 (to 20 lakh), 1.8 (larger)
Example: A town of 1,00,000 at 135 lpcd: Average daily demand = 13.5 MLD.
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Rainwater Harvesting Calculator
V = A × R × C
A roof area (m²), R rainfall (m), C runoff coefficient
Example: A 200 m² roof with 800 mm of rain a year: Harvestable water per year = 122400 L.
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- Stopping Sight Distance Calculator – Design speed, reaction time, friction and gradient → SSD.
- Traffic Flow Calculator – Free speed, jam density and density → speed, flow, capacity and headways.
Building Services and Sustainability
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Reverberation Time Calculator
T₆₀ = 0.161 V / ΣSα
Eyring: T = 0.161 V / (−S ln(1 − ᾱ))
Example: A 1000 m³ hall with 200, 200 and 300 m² of surfaces at α = 0.02, 0.3 and 0.1: Reverberation time (Sabine) T₆₀ = 1.71277 s.
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Lumen Method Calculator
N = E A / (F n UF MF)
room index K = LW / (Hm(L + W))
Example: A 10 × 8 m office lit to 300 lux with twin 3000 lm luminaires, UF 0.6 and MF 0.8: Number of luminaires N = 8.33333.
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Air Changes per Hour Calculator
Q = ACH × V
Q in m³/h, V room volume in m³
Example: A 6 × 5 × 3 m room at 6 air changes per hour: Airflow = 540 m³/h.
Unit Converters for GATE Architecture (AR)
- R-Value Converter (US R to RSI, m²·K/W) – US R-value, RSI, clo, tog
- Illuminance Converter (Lux, Foot-candle) – lux, foot-candles, klx, phot
- Area Converter – m², cm², mm², ft², in², test areas
- Angle Converter – degrees, radians, gradians, arcminutes
Common GATE Architecture (AR) Conversions
How to use these GATE Architecture and Planning calculators
GATE Architecture and Planning includes a growing share of numerical questions on development controls, building physics and services. This hub collects calculators for floor area ratio and ground coverage, gross and net residential density, Sabine and Eyring reverberation time, the U-value of walls and roofs, the lumen method, air changes per hour, solar altitude and azimuth, staircase and ramp design, town water demand with CPHEEO peak factors, rooftop rainwater harvesting and years’ purchase valuation, plus the shared CPM, PERT, population-forecast and traffic tools.
Indian norms are used where the syllabus expects them: NBC 2016 for risers, treads and ramps, CPHEEO for water supply and peak factors, and URDPFI ranges for densities. Each page gives the formula, a worked example and the full result.
The R-value converter on this page translates US insulation ratings into m²·K/W for U-value calculations, and the illuminance converter handles lux and foot-candles for lighting questions.