Health

Calculate the Glasgow Coma Scale (GCS) from the three response components: Eye Opening (E, 1–4), Verbal Response (V, 1–5), and Motor Response (M, 1–6). Total = E + V + M, range 3–15. Supports the '1t' notation for intubated/untestable verbal response (counted as V = 1, with an annotation, and recommends reporting the E_M_V component string). Severity bands: 13–15 mild, 9–12 moderate, 3–8 severe (severe scores commonly prompt airway protection). Derived from Teasdale & Jennett, Lancet 1974, with the Lancet Neurology 2014 review and 2024 update. Not medical advice.

Health

Calculate the Fractional Excretion of Sodium (FENa) to differentiate prerenal from intrinsic acute kidney injury: FENa (%) = [U_Na × S_Cr] / [S_Na × U_Cr] × 100. In oliguric AKI, FENa <1% suggests prerenal azotemia (sodium-avid state: volume depletion, heart failure, hepatorenal syndrome), while FENa ≥1% suggests intrinsic injury (typically ATN). FENa >4% is sometimes cited as supportive of post-obstructive pathology. Caveats: unreliable on diuretics (use FEUrea <35%), contrast/sepsis ATN can present with low FENa, chronic CKD and glucosuria elevate FENa independently. Derived from Espinel CH, JAMA 1976. Most useful in oliguric AKI; interpret with full clinical context. Not medical advice.

Math & Numbers

Convert force between newton (N, SI base), kilonewton (kN), dyne (dyn, CGS = 10⁻⁵ N), pound-force (lbf = 4.4482216152605 N), kilogram-force (kgf = 9.80665 N), and poundal (pdl = 0.138254954376 N). All factors derive from the exact defining constants 1 lb = 0.45359237 kg, 1 ft = 0.3048 m, and standard gravity g₀ = 9.80665 m/s². Converts via newton to the target unit and lists the equivalent value in all six units. Reference: 1 kg of mass on Earth ≈ 9.80665 N (1 kgf); an adult weighs ≈ 700 N.

Math & Numbers

Convert fuel consumption / fuel economy between L/100km, miles per US gallon (mpg US), miles per Imperial gallon (mpg UK), and km/L. mpg and L/100km are reciprocal (higher mpg = lower L/100km), so conversion goes through the km/L axis, not a single multiplier. Defining constants are exact by law: 1 US gallon = 3.785411784 L (NIST HB 44), 1 Imperial gallon = 4.54609 L (UK W&M Act 1985), 1 mile = 1.609344 km (1959 agreement). Reference: a compact car at ~6 L/100km ≈ 39 mpg US ≈ 47 mpg UK.

Math & Numbers

Estimate multi-segment trip fuel, cost, CO2, route-condition weighting, and carpool sharing.

Math & Numbers

Calculate the gear module m. m = d/z = p/π. Solve the module from the pitch diameter d and tooth count z, or from the circular pitch p. Also returns the pitch diameter, circular pitch and addendum.

Math & Numbers

Calculate the gear ratio and output speed of a meshing gear pair. i = z₂/z₁ = n₁/n₂. Enter the tooth counts to get the ratio; add the driver speed to get the driven speed.

Math & Numbers

Calculate the overall ratio and output speed of a multi-stage gear train. i_total = i₁·i₂·…·iₙ (each i = z₂/z₁). Enter tooth pairs per stage and the input speed to get the final output speed.

Finance

Project today's amount (plus optional recurring contributions) forward with compound interest (FV). Supports a lump sum or lump sum + annuity, multiple compounding frequencies, a growth curve, and a per-period breakdown. FV = PV*(1+r)^n for a lump sum.

Math & Numbers

Convert between frequency and wavelength with selectable medium; results in all common frequency and length units

Math & Numbers

Compute distance, time, or final velocity for free fall from rest, given any one plus gravity

Math & Numbers

Compute force, mass, or acceleration from Newton's second law, with weight on Earth