Health

Calculate solute-free water clearance (C_H₂O) and electrolyte-free water clearance (eC_H₂O) to differentiate hypo-/hypernatremia. Classic: C_H₂O = V·(1 − U_osm/P_osm); positive = dilute urine excreting free water (diabetes insipidus, polydipsia, water-load recovery), negative = concentrated urine conserving free water (dehydration, SIADH). Electrolyte-free: eC_H₂O = V·(1 − (U_Na + U_K)/P_Na), which better predicts the direction of serum sodium change — a negative eC_H₂O means the urine is electrolyte-free-water-rich and tends to raise serum Na⁺, informing IV fluid choice. Optional Na/K inputs enable the electrolyte-free calculation. Derived from Rose, Shimizu 2002 (Nephron), and NephSIM. Point estimate; interpret with full clinical context. Not medical advice.

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.

Design

Preview a heading and body font pairing with real copy, sizes, weights, line heights, character samples, and CSS stacks.

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

Convert mass flow rate between kg/s (kilograms per second, SI base), lb/h (pounds per hour, 1 lb = 0.45359237 kg), and t/h (tonnes per hour, 1 t = 1000 kg). Converts via kg/s to the target unit and also lists the equivalent value in all three units for reference. Used for boiler feedwater, chemical dosing, fuel consumption, and compressed-gas metering.

Math & Numbers

Convert volumetric flow rate between m³/h (cubic metres per hour), L/min (litres per minute), gpm (US gallons per minute, 1 gal = 3.785411784 L), and cfm (cubic feet per minute, 1 ft³ = 28.3168466 L). Converts via m³/s to the target unit and also lists the equivalent value in all four units for reference. Used for pumps, HVAC, compressed air, and piping.

Math & Numbers

Mean-stress fatigue correction under cyclic loading. Given stress amplitude σ_a, mean stress σ_m, and material σ_uts / σ_-1 (endurance limit) / σ_y, compute safety factors from three classical criteria: Modified Goodman (linear, conservative), Gerber (parabolic, better for ductile metals), and Soderberg (uses σ_y, most conservative). Reports the governing (smallest) value and whether the operating point lies inside the Goodman line.

Data Processing

Evaluate bounded Excel-style formulas against JSON cell values and explain results, references, and spreadsheet errors.

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.