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Browse the tool catalog | Page 153

Search and filter the online tool directory by task, format, and category, then open detailed pages with clear inputs, examples, and execution context. Page 153.

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Math, Date & Finance586

Calculators, numerics, date logic, statistics, and finance tools

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Health

Drug Clearance Calculator (CL)

Calculate drug clearance CL in two modes. (A) Definition: CL = elimination rate / concentration, valid for any pharmacokinetic model. (B) Linear first-order: CL = k · Vd (or derive k from t½ via k = ln2 / t½). Also reports the relationship t½ = 0.693 · Vd / CL. CL is a definitional parameter independent of Vd. Linear mode applies only to first-order elimination — NOT to Michaelis-Menten drugs (phenytoin, high-dose ethanol). Reference: theophylline CL ≈ 2.8 L/h in a 70 kg non-smoking adult. Not medical advice.

Health

Drug Half-Life Concentration Calculator

Estimate plasma drug concentration at a chosen time after an IV bolus using a one-compartment model with first-order elimination: C(t) = (Dose / Vd) · e^(-k·t), where k = ln2 / t½. Includes initial concentration C0, elimination rate constant k, percent remaining, and number of half-lives elapsed. Valid only for linear pharmacokinetics — NOT for Michaelis-Menten drugs (phenytoin, high-dose ethanol) or multi-compartment distribution. Reference: theophylline Vd ≈ 0.45 L/kg, t½ ≈ 8 h. Not medical advice.

Math & Numbers

Dynamic Viscosity Converter (Pa·s / cP / lbf·s/ft²)

Convert dynamic (absolute) viscosity between Pa·s (pascal-second, SI base, = N·s/m² = kg/(m·s)), cP (centipoise, 1 cP = 0.001 Pa·s), and lbf·s/ft² (imperial, 1 = 47.88025898 Pa·s). Converts via Pa·s to the target unit and also lists the equivalent value in all three units for reference. Reference values: water 20°C ≈ 1.002 cP, glycerol 20°C ≈ 1412 cP, air 20°C ≈ 0.0181 cP.

Math & Numbers

Dew Point Calculator HVAC (Magnus Equation)

Compute the air dew-point temperature from dry-bulb temperature and a humidity reading using the Magnus saturation-pressure equation: P_ws(T) = 0.6108·exp(17.27·T/(T+237.3)), P_w = φ·P_ws, T_dp = 237.3·ln(P_w/0.6108) / (17.27 − ln(P_w/0.6108)). Also returns the saturation vapour pressure P_ws, actual partial pressure P_w, and absolute humidity ρ_v (kg/m³). Three input modes: relative humidity φ (natural ventilated), August natural-ventilated wet-bulb T_w, or aspirated (Assmann) wet-bulb T_wa. Temperature in °C/K/°F; all reported temperatures are in the selected Temperature Unit.

Math & Numbers

Drag Force Calculator (F_D = ½·ρ·v²·C_D·A)

Compute the drag force on a body in a fluid stream: F_D = ½·ρ·v²·C_D·A (N), where ρ is the fluid density, v the free-stream velocity, C_D the drag coefficient (shape- and Reynolds-dependent), and A the reference (frontal projected) area. A built-in shape library supplies typical high-Re C_D values: sphere 0.47, hemisphere 0.42, long cylinder 0.81, disk/flat plate 1.17, cube 1.05, streamlined airfoil 0.04, long streamlined ellipsoid 0.07, cone 0.50; or choose 'Custom' to enter C_D directly. Optionally, with dynamic viscosity μ and characteristic length L, the Reynolds number Re = ρ·v·L/μ is computed, and the power dissipated by drag P = F_D·v (W). Density in kg/m³/g/cm³, velocity in m/s/km/h, area in m²/cm²/mm², length in m/cm/mm.

Math & Numbers

Duct Size Calculator (Flow Rate × Velocity)

Size a duct cross-section from the air flow rate Q and the design mean velocity v: area A = Q/v. Circular duct diameter D = √(4A/π). Rectangular duct with aspect ratio r = a/b gives b = √(A/r) and a = r·b, plus the ASHRAE equivalent diameter D_eq = 1.30·(a·b)^0.625/(a+b)^0.25. Flow rate in m³/s/m³/h/CFM, velocity in m/s; dimensions reported in mm and inches.

Math & Numbers

EER ↔ SEER ↔ COP Converter (Refrigeration Efficiency)

Convert between the three common refrigeration efficiency metrics: COP (dimensionless, W/W), EER (Btu/(W·h)), and SEER (seasonal Btu/(W·h)). Standard relations: COP = EER / 3.412, EER = COP × 3.412, SEER = EER / α (α seasonal weighting factor, default 0.875, adjustable 0.8–0.91 to match regional standards such as ARI 210/240). Enter any one metric and all three are reported.

Math & Numbers

Cylinder Radial Heat Conduction (Q=2πkL·ΔT/ln(r₂/r₁))

Compute radial steady-state heat conduction through a single-layer cylindrical wall (Fourier's law in cylindrical coordinates): radial heat flow rate Q = 2π·k·L·ΔT/ln(r₂/r₁) (W), inner-surface heat flux q_inner = Q/(2π·r₁·L) (W/m²), outer-surface heat flux q_outer = Q/(2π·r₂·L) (W/m²), and cylindrical thermal resistance R = ln(r₂/r₁)/(2π·k·L) (K/W). k is the thermal conductivity (W/(m·K)); L the cylinder length; r₁ the inner radius, r₂ the outer radius (must have r₂ > r₁ > 0); ΔT the temperature difference (K; a °C difference equals a K difference, a °F difference is converted by ×5/9). ΔT may be negative (indicating reverse heat flow), but k, L, r₁ and r₂ must be positive. Length and radius in m/cm/mm.

Math & Numbers

DC Motor Back-EMF & Torque Calculator (E=kω, T=kI)

Compute the back-EMF and electromagnetic torque of a DC motor from its machine constant: E=k·ω, T=k·I. In SI units the back-EMF constant equals the torque constant (k_e=k_t=k, V·s/rad=N·m/A). Also returns the mechanical (air-gap) power P=T·ω=E·I. Speed accepted in rad/s or RPM.

Data Processing

Excel Formula Evaluator

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

Math & Numbers

Beam Deflection Calculator

Look up and compute the maximum deflection for four classic beam cases: cantilever with end point load (δ=PL³/3EI), cantilever with UDL (δ=qL⁴/8EI), simply supported with mid-span point load (δ=PL³/48EI), and simply supported with UDL (δ=5qL⁴/384EI).

Math & Numbers

Dimensional Analysis Unit Cancellation Tutor

Step-by-step factor-label unit cancellation with inverted-factor diagnosis and optional student-answer checking.