Math & Numbers

Estimate the saturated condensing temperature (T_cond) and evaporating temperature (T_evap) of a refrigeration circuit. Three modes: (1) from coil approach — T_cond = T_ambient + condenser ΔT approach, T_evap = T_medium − evaporator ΔT approach; (2) from measured saturated pressures — given P_cond and P_evap for a known refrigerant (R-22 / R-134a / R-410A), invert the Antoine fit; (3) from subcooling & superheat — T_cond = T_liquid − SC, T_evap = T_suction − SH. Temperature in °C/K/°F; pressure in bar/MPa/kPa/PSI absolute or gauge (atmospheric default 1.01325 bar). Results reported in °C.

Math & Numbers

Solve the Bernoulli equation p/(ρg) + v²/(2g) + z = const for steady, ideal, incompressible flow between two points on a streamline. Supply all three upstream quantities (p₁, v₁, z₁) and any two of the three downstream quantities; the tool solves for the third. Solve velocity: v₂ = √[v₁² + 2(p₁-p₂)/ρ + 2g(z₁-z₂)] — a negative radicand is physically impossible and is rejected. Solve pressure: p₂ = p₁ + ½ρ(v₁²-v₂²) + ρg(z₁-z₂). Solve elevation: z₂ = z₁ + (p₁-p₂)/(ρg) + (v₁²-v₂²)/(2g). g = 9.81 m/s². Density in kg/m³/g/cm³, pressure in Pa/kPa/bar/atm/psi, velocity in m/s, elevation in m/cm/ft. The upstream pressure/velocity/elevation heads and the total head are also reported.

Math & Numbers

Estimate the cooling load of a room by the simplified ASHRAE steady-state method. Transmission sensible load Q_trans = Σ(A_i·U_i·ΔT) over envelope surfaces entered one per line as 'area,U' (U in W/(m²·K)). Infiltration/ventilation sensible Q_s = 1.23·ACH·V·ΔT and latent Q_l = 3010·ACH·V·ΔW (W), where ΔW is the indoor-outdoor humidity-ratio difference derived from dry-bulb temperature and relative humidity via the Magnus saturation fit. Total cooling load = total sensible + total latent. Temperature in °C/K/°F (only differences matter), area in m²/ft².

Math & Numbers

Compute the Coefficient of Performance (COP) of a chiller / heat pump: COP = Q_c / W, where Q_c is the cooling capacity and W the work input (both in consistent power units; COP is dimensionless). Three modes: solve COP (given Q_c and W), solve cooling capacity (given COP and W), or solve input power (given COP and Q_c). Capacity in W/kW/BTU·h⁻¹/ton/kcal·h⁻¹, power in W/kW/hp; all converted to W internally.

Math & Numbers

Estimate copper cable current-carrying capacity per the simplified IEC 60364-5-52 reference method. Combines cross-section, insulation (PVC 70°C / XLPE 90°C), installation method, and ambient temperature to derive the corrected allowable ampacity (A).

Math & Numbers

Compute the reactive power produced by a known capacitor: Q_c = 2π·f·C·U². Supports single-phase, three-phase star (Y) and delta (Δ) connections. Returns Q_c in var/kvar, capacitive reactance Xc, and capacitor current Ic. Complementary to the power-factor-correction tool (which sizes a capacitor for a target cosφ).

Math & Numbers

Calculate support reactions of a simply supported beam via static equilibrium. UDL: RA=RB=q·L/2. Center point load: RA=RB=P/2. Off-center point load at a: RA=P·b/L, RB=P·a/L. Also returns max shear Vmax and max moment Mmax.

Math & Numbers

Calculate the Terzaghi ultimate bearing capacity of a shallow foundation: q_ult = c·Nc·sc + q·Nq·sq + 0.5·γ·B·Nγ·sγ. Computes Nc/Nq/Nγ and shape factors automatically; supports strip, square, and circular footings. Result in kPa.

Math & Numbers

Calculate the Euler critical buckling load of an axially loaded column: P_cr = π²·E·I/(K·L)². Supports pinned-pinned (K=1), fixed-free (K=2), fixed-pinned (K=0.7), fixed-fixed (K=0.5). Returns effective length, radius of gyration, slenderness ratio λ, and critical stress σ_cr.

Math & Numbers

Convert between concrete strength notations: C grade ↔ cube strength fcu ↔ cylinder fck,cyl ↔ prism fck,prism ↔ design value fc. Ratios: fck,cyl = 0.8·fcu, fck,prism = 0.88·0.76·fcu, fc = fck,prism/1.4. Any one input produces all others.

Math & Numbers

Calculate the maximum bending (flexural) stress σ_max = M·c/I = M/Z at the outermost fiber of a beam section. Supports solid circle, rectangle, hollow tube, and I-beam; computes I, section modulus Z, and distance c automatically. Stress in MPa.

Math & Numbers

Calculate the maximum bending moment M_max, maximum shear force V_max and free-end deflection δ_max of a cantilever beam under a free-end point load P or a uniformly distributed load q. Point load: δ = PL³/(3EI); UDL: δ = qL⁴/(8EI).