Math & Numbers

Convert sound power between linear units (W, mW, µW, pW) and the decibel sound power level dB Lw (Lw = 10·log₁₀(W / 1 pW), reference P₀ = 1 pW = 1e-12 W, per ISO 3744 / IEC 60027-3). Supports bidirectional linear↔logarithmic conversion and reports the equivalent value in all five units. Reference values: whisper ≈ 1e-9 W (Lw ≈ 30), speech ≈ 1e-5 W (Lw ≈ 70), jet engine at 1 m ≈ 1e4 W (Lw ≈ 160).

Math & Numbers

Convert sound pressure between linear units (Pa, µPa, µbar, mbar) and the decibel sound pressure level dB SPL (Lp = 20·log₁₀(p / 20 µPa), reference p₀ = 20 µPa = 2e-5 Pa RMS, per ISO 1683). Supports bidirectional linear↔logarithmic conversion. Calibration anchor: 1 Pa → 20·log₁₀(1/2e-5) ≈ 94 dB SPL. Reference values: threshold of hearing 20 µPa (0 dB), speech ≈ 0.02 Pa (60 dB), rock concert ≈ 20 Pa (120 dB), pain threshold ≈ 200 Pa (140 dB).

Math & Numbers

Convert specific heat capacity between J/(kg·K) (joule per kilogram-kelvin, SI base, = J/(kg·°C)), kcal/(kg·°C) (1 = 4186.8 J/(kg·K)), and BTU/(lb·°F) (1 = 4186.8 J/(kg·K)). Key identity: 1 kcal/(kg·°C) = 1 BTU/(lb·°F) — numerically equal because the energy/mass·temperature factors cancel. Converts via J/(kg·K) and lists all three equivalents. Reference values: water ≈ 4186, air cp ≈ 1005, aluminum ≈ 900, iron ≈ 450 J/(kg·K).

Math & Numbers

Specific strength = σ/ρ and specific modulus = E/ρ (optional E). Enter strength in MPa and density in g/cm³; output in N·m/kg (also as kN·m/kg). The figure of merit for lightweight design — a material with high strength but high density (e.g. tungsten) often loses to a lighter alloy. Typical values: Ti-6Al-4V ≈ 210 kN·m/kg, Al 7075 ≈ 180, carbon steel ≈ 50–90, CFRP ≈ 1000+.

Math & Numbers

Calculate the static safety factor n = σ_limit / σ_applied against yielding (σ_y) or ultimate tensile strength (σ_uts). Built-in typical strengths for carbon/alloy steel, aluminum, copper, austenitic stainless and titanium, plus a custom σ_limit option. Assessment: n<1 failure, 1≤n<1.5 marginal, n≥1.5 safe.

Math & Numbers

Calculate engineering stress σ = F/A and engineering strain ε = ΔL/L₀ under uniaxial load. Choose what to solve: for stress, enter force F (N) and cross-section area A (mm²) → result in MPa; for strain, enter original length L₀ and elongation ΔL (negative for compression) → dimensionless ratio. Units are self-consistent (N, mm) so stress comes out directly in MPa.

Math & Numbers

Split an air-conditioning load into sensible and latent components. Total cooling capacity Qt = ṁ_da·(h1 − h2); sensible capacity Qs = ṁ_da·cp_ma·(T1 − T2) with cp_ma ≈ 1.006 + 1.86·W [kJ/(kg da·K)]; latent capacity Ql = Qt − Qs; Sensible Heat Ratio SHR = Qs / Qt. Entering/leaving states are described by dry-bulb temperature T and humidity ratio W; enthalpy h = 1.006·T + W·(2501 + 1.86·T) [kJ/kg da]. Three modes: full air-state split (T1,W1)→(T2,W2), from Qt & Qs (solve SHR + Ql), or from Qt & SHR (solve Qs, Ql).

Math & Numbers

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

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

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

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

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.