Estimate the three-phase symmetric short-circuit current using the IEC 60909 far-from-generator method: I"_k = c·U_n/(√3·|Z|) and i_p = κ·√2·I"_k with κ = 1.02 + 0.98·e^(−3R/X). Source impedance is the series sum of transformer and line R/X.

Math & Numbers

Power Factor Correction Calculator

Size the shunt capacitor needed to raise the power factor: C = P·(tanφ₁ − tanφ₂)/(2π·f·U²). Returns compensated reactive power Qc, capacitive reactance Xc, capacitor current Ic, and the required capacitance in F/μF.

Math & Numbers

Section Modulus Calculator

Calculate the elastic section modulus W = I/y_max and associated geometric properties. Supports rectangle, solid circle, hollow tube, and I-beam; computes I, distance c, area A, and radius of gyration r. Units in mm.

Math & Numbers

Slope Stability Calculator (Infinite Slope)

Calculate the infinite-slope factor of safety: FS = c'/(γ·z·cosβ·sinβ) + tanφ'/tanβ. Supports dry slopes and seepage parallel to the slope. Returns FS and a stable/marginal/unstable classification.

Math & Numbers

Three-Phase Power Calculator

Calculate active, reactive, and apparent power for a balanced three-phase system: S=√3·U·I, P=√3·U·I·cosφ, Q=√3·U·I·sinφ. Also returns the power-factor angle φ and verifies the power triangle.

Math & Numbers

Active Earth Pressure (Rankine)

Calculate the Rankine active earth pressure on a smooth vertical wall backfilled with cohesionless soil. K_a = tan²(45°−φ/2). Optional uniform surcharge q. Returns the base pressure p₀, the total force P, and the resultant height.

Math & Numbers

Rebar Area Calculator

Calculate the total cross-sectional area of reinforcing steel: A = n·π·D²/4. Choose a standard metric diameter (6–40 mm) or a custom diameter and the number of bars. Also returns the single-bar area, perimeter, theoretical unit weight (ρ=7850 kg/m³), and total weight.

Math & Numbers

Shear Stress Calculator

Calculate the maximum shear stress τ_max = V·Q/(I·b) at the neutral axis of a beam section. Supports rectangle (1.5V/A), solid circle (4V/3A), hollow tube, and I-beam (exact V·Q_web/(I·tw)). Also returns the average shear stress V/A for comparison.

Math & Numbers

Simply Supported Beam Calculator

Calculate the maximum bending moment M_max, maximum shear force V_max and support reactions for a simply supported beam under a uniformly distributed load, a mid-span point load, or a point load at an arbitrary position. UDL: M_max = qL²/8; mid-span: M_max = PL/4; offset: M_max = P·a·b/L.

Math & Numbers

Power Transmission Efficiency Calculator

Calculate the overall efficiency of a multi-stage transmission. η_total = η₁·η₂·…·ηₙ. Enter one stage efficiency per line (decimal, e.g. 0.98). Optionally add an input power to get the total loss and per-stage output power.

Math & Numbers

Shaft Critical Speed Calculator

Calculate the critical (resonance) speed of a rotating shaft using the single-DOF rotor model. ω_n = √(k/m), n_cr = (60/2π)·√(k/m) rpm. Also returns the natural frequency f_n in Hz.

Math & Numbers

Shaft Power Calculator

Calculate the power transmitted by a rotating shaft. P = T·ω = 2π·n·T/60. Solve power from torque and speed, or torque from power and speed. Supports W/kW/hp.