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

Sound Pressure Level Converter (Pa / dB SPL re 20 µPa)

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

Specific Heat Capacity Converter (J/(kg·K) / kcal / BTU)

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 & Specific Modulus Calculator

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

Stress & Strain Calculator

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

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

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

Spring Compression Energy Calculator

Calculate the elastic potential energy and force of a spring in compression or extension. U = ½·k·x², F = k·x. Solve energy from displacement, or displacement from energy.

Math & Numbers

Spring Rate Calculator

Calculate the stiffness (spring rate) of a cylindrical helical compression/extension spring. k = G·d⁴ / (8·D³·n) in N/mm. Includes shear-modulus presets for common spring materials.

Math & Numbers

Significant Figures Sandbox

Practice significant-figure rules with step-by-step feedback: count sig figs, round to N sig figs, convert to scientific notation, and propagate through +/−/×/÷.

Math & Numbers

Square Meter to Hectare

Convert square meters to hectares with configurable decimal precision