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Formula solvers — N

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Napier's Steam Leak Rate

m˙=A P70\dot{m} = \frac{A \, P}{70}

ThermodynamicsWater TreatmentFluid MechanicsSteam lost through a hole, a blowing trap or a lifted relief valve by Napier's rule — pounds per second from square inches times psia, over 70.

Narrow-Sense Heritability

h2=VAVPh^2 = \frac{V_A}{V_P}

Plant Breeding & GeneticsThe additive share of phenotypic variance — the only part that reliably passes from parent to offspring, and the one the breeder's equation uses.

Natural Frequency from Static Deflection

fn=12πgδstf_n = \frac{1}{2\pi} \sqrt{\frac{g}{\delta_{st}}}

Machine DesignThe natural frequency read off the amount the mount sinks under the weight it carries — no spring rate needed, because the weight already measured it. The fastest sanity check in isolation work.

NDVI — Normalized Difference Vegetation Index

NDVI=ρNIR−ρredρNIR+ρred\mathrm{NDVI} = \frac{\rho_{NIR} - \rho_{red}}{\rho_{NIR} + \rho_{red}}

Photogrammetry & Remote SensingThe oldest and most-used vegetation index: near-infrared reflectance minus red, over their sum. Healthy leaves absorb red for photosynthesis and scatter near-infrared strongly, so the difference tracks green canopy. Defined by Rouse, Haas, Schell and Deering in NASA SP-351 (1974) page 309, from ERTS-1 imagery of the Great Plains.

Negative Likelihood Ratio (LR−)

LR−=1−SeSp\mathrm{LR^-} = \frac{1 - \mathrm{Se}}{\mathrm{Sp}}

Epidemiology & Diagnostic AccuracyHow many times more often a negative result turns up in someone with the condition than in someone without it. Below 1 it lowers the odds; the further below, the more a negative result rules out.

Negative Predictive Value (NPV)

NPV=TNTN+FN\mathrm{NPV} = \frac{\mathrm{TN}}{\mathrm{TN} + \mathrm{FN}}

Epidemiology & Diagnostic AccuracyOf everyone the test called negative, the share who genuinely do not have the condition — read along the test-negative ROW of a 2×2 table.

Nernst Equation

E=E∘−RTnFln⁡QE = E^{\circ} - \frac{RT}{nF}\ln Q

ChemistryCorrects a cell's standard potential for non-standard concentrations, the equation behind every pH meter, ion-selective probe, and battery voltage curve.

Nernst Equilibrium Potential for a Membrane Ion (37 °C)

Eion=61.5zlog⁡10CoutCinE_{ion} = \frac{61.5}{z}\log_{10}\frac{C_{out}}{C_{in}}

Biomedical & ClinicalThe membrane voltage at which an ion's electrical and chemical driving forces cancel, in the millivolt form physiologists use at 37 °C.

Net Allowable Bearing Pressure

qall=qu−qFSq_{all} = \frac{q_u - q}{FS}

Soil MechanicsMechanicsNet allowable bearing pressure for a footing, the ultimate capacity less the existing overburden, divided by the chosen factor of safety.

Net Irrigation Requirement

IRn=ETc−PeIR_n = ET_c - P_e

Crop ProductionThe depth of water irrigation must supply over a period: everything the crop used, less the rainfall that actually reached the root zone. The word doing the work is effective — rain that ran off or drained past the roots is not in this equation.

Net Positive Suction Head Available (NPSHa)

NPSHa=hatm+hs−hf−hvpNPSH_a = h_{atm} + h_s - h_f - h_{vp}

HVAC & HydronicsFluid MechanicsWater TreatmentAbsolute head available at the pump suction above the liquid's vapour pressure — the margin that keeps a pump from cavitating.

Net Present Value of a Uniform Annual Cash Flow

NPV=A 1−(1+i)−ni−C0\mathit{NPV} = A\,\frac{1 - (1+i)^{-n}}{i} - C_0

Industrial EngineeringMoney & BusinessWorth of a project today when it costs C0 up front and returns the same net amount every year for n years: the discounted value of the series, less what it cost to start.

Net Radiation Exchange Between Surfaces

Q˙=εσA(T14−T24)\dot{Q} = \varepsilon \sigma A (T_1^4 - T_2^4)

Heat TransferThermodynamicsNet radiant heat from a grey surface to large surroundings, using the Stefan-Boltzmann constant and the difference of fourth-power temperatures.

Net Radiative Cooling to the Sky

qnet=εσ(Ts4−Tsky4)q_{net} = \varepsilon \sigma \left(T_s^{4} - T_{sky}^{4}\right)

Heat TransferThermodynamicsNet longwave heat lost per square metre from a surface facing the open sky, as the difference of fourth powers between the surface and the effective sky temperature. On a clear night this runs to 60-100 W/m², which is what pulls a surface below air temperature.

Net Water and Sewer Cost of a Cooling Tower

C=Vm pw+(Vm−Ve) psC = V_m \, p_w + (V_m - V_e) \, p_s

Water TreatmentFluid MechanicsWater & WastewaterFull water and sewer bill for a cooling tower: makeup charged at the water rate, plus only the volume actually discharged at the sewer rate.

Newton's Law of Cooling (Q = hAΔT)

Q˙=hA ΔT\dot{Q} = h A \, \Delta T

Heat TransferThermodynamicsHVAC & HydronicsConvective heat rate from a surface, set by the film coefficient, the wetted area and the surface-to-fluid temperature difference.

Newton's Law of Universal Gravitation

F=Gm1m2r2F = \frac{G m_1 m_2}{r^2}

MechanicsPhysicsAttractive force between two masses, with G = 6.6743 × 10⁻¹¹ m³ kg⁻¹ s⁻² (CODATA 2018).

Newton's Second Law

F=maF = m a

PhysicsForce equals mass times acceleration.

Newton's Second Law for Rotation (τ = Iα)

τ=Iα\tau = I \alpha

MechanicsPhysicsNet torque equals moment of inertia times angular acceleration — F = ma for spinning things.

Nitrogen in Anhydrous Ammonia

N=0.8224×NH3N = 0.8224 \times NH_3

Crop ProductionThe elemental nitrogen carried by a mass of anhydrous ammonia — 82.2% by weight, the highest-analysis nitrogen fertiliser there is.

Nitrogen Use Efficiency

NUE=Yf−Y0RnNUE = \frac{Y_f - Y_0}{R_n}

Crop ProductionExtra yield produced per unit of nitrogen applied, measured against an unfertilised control. The agronomic efficiency figure that decides whether the last increment of nitrogen paid.

Noise Reduction Coefficient (NRC)

NRC=α250+α500+α1000+α20004\mathrm{NRC} = \frac{\alpha_{250} + \alpha_{500} + \alpha_{1000} + \alpha_{2000}}{4}

Acoustics & NoiseThe single number on an acoustic panel's data sheet: the plain average of its absorption coefficients in the 250, 500, 1000 and 2000 Hz octave bands, rounded to the nearest 0.05. Convenient, widely quoted, and it hides everything that happens below 250 Hz.

Non-Inverting Op-Amp Gain

G=1+RfRinG = 1 + \frac{R_{f}}{R_{in}}

Electrical TradeElectricity & MagnetismClosed-loop gain of a non-inverting operational amplifier, always one more than the feedback-to-ground resistor ratio.

Normal (Axial) Stress

σ=PA\sigma = \frac{P}{A}

Strength of MaterialsMechanicsPhysicsAxial stress in a bar or hanger rod — the internal force divided by the cross-sectional area that carries it, in Pa or psi.

Normal Force on an Incline (N = mg cos θ)

N=mgcos⁡θN = m g \cos\theta

MechanicsPhysicsNormal force pressing a resting mass into an incline, equal to the component of its weight perpendicular to the slope.

Normal Probability Density

f(x)=1σ2πe−(x−μ)22σ2f(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{(x - \mu)^{2}}{2\sigma^{2}}}

StatisticsAlgebraThe height of the normal bell curve at a given value, set by the distance from the mean in standard deviations.

Normal Strain (ε = δ/L)

ε=δL\varepsilon = \frac{\delta}{L}

Strength of MaterialsMechanicsPhysicsNormal strain as the change in length divided by the original length, a dimensionless ratio usually quoted in microstrain.

Normalised Enthalpy and the Keyhole Threshold

ΔHhs=A Phs π D v σ3\frac{\Delta H}{h_s} = \frac{A \, P}{h_s \, \sqrt{\pi \, D \, v \, \sigma^{3}}}

Additive ManufacturingThe dimensionless group King and colleagues at Lawrence Livermore put forward in 2014 to predict when a laser stops melting and starts drilling. It compares the energy the beam actually deposits into the interaction volume with the energy needed to bring that material to its melting point — and unlike volumetric energy density it keeps power, speed and spot size in the arrangement the heat-conduction physics puts them in, which is why it works and E_v does not.

Normality from Molarity

N=M×neqN = M \times n_{\text{eq}}

ChemistryConverts molarity into normality by multiplying by the number of reactive equivalents each mole of solute supplies.

Norton Creep Law

ε˙=A σ nexp⁡ ⁣(−QRT)\dot{\varepsilon} = A \, \sigma^{\,n} \exp\!\left( -\dfrac{Q}{RT} \right)

Metallurgy & Heat TreatmentSteady-state creep, written as a power law in stress multiplied by an Arrhenius term in temperature. Norton put the stress dependence down in 1929 and the Arrhenius factor came from Dorn's work, and between them the two exponents identify WHICH creep mechanism is running — which is the real reason to fit them.

Norton Current from the Thevenin Equivalent

IN=VThRThI_{N} = \frac{V_{Th}}{R_{Th}}

Electricity & MagnetismElectrical TradeEvery Thevenin source has an identical Norton twin: the same resistance in parallel, driven by the current the source would deliver into a dead short.

Nozzle Area Ratio and Mach Number

AA∗=1M[2γ+1(1+γ−12M2)]γ+12(γ−1)\frac{A}{A^{*}} = \frac{1}{M}\left[\frac{2}{\gamma+1}\left(1 + \frac{\gamma-1}{2}M^{2}\right)\right]^{\frac{\gamma+1}{2(\gamma-1)}}

Aerospace & FlightThe isentropic relation between how far a nozzle has opened out and how fast the gas is moving there. It is what turns a throat into supersonic exhaust, and the reason a rocket nozzle is a bell rather than a hole.

Nozzle Output at a New Pressure

Q2=Q1p2p1Q_2 = Q_1 \sqrt{\frac{p_2}{p_1}}

Crop ProductionHow a spray nozzle's output changes when the pressure changes: flow rises with the square root of pressure, so doubling the output takes four times the pressure.

Nozzle Output Deviation

D=100 Qm−QrQrD = 100 \, \frac{Q_m - Q_r}{Q_r}

Crop ProductionHow far a nozzle has drifted from its rated output, as a percentage. The standard check before spraying: worn nozzles pass more than they should, and the trade replaces them at ten percent over.

nth Root as a Fractional Exponent

y=xn=x1/ny = \sqrt[n]{x} = x^{1/n}

AlgebraThe nth root of a number written as a fractional exponent, so that roots and powers obey exactly the same set of rules.

Nuclear Radius (r = r₀A^⅓)

r=r0A1/3r = r_0 A^{1/3}

Modern PhysicsPhysicsRadius of a nucleus of mass number A: r₀ times the cube root of A, because nuclear matter packs at one fixed density.

Number Needed to Treat (NNT)

NNT=1CER−EER\mathrm{NNT} = \frac{1}{\mathrm{CER} - \mathrm{EER}}

Epidemiology & Diagnostic AccuracyHow many people have to receive the treatment for one of them to avoid the outcome — the reciprocal of the absolute risk reduction. It is a trial summary, not a prescription: it counts people, and this shard computes no dose.

Number of Modes in a Step-Index Fibre

M≈V22M \approx \frac{V^{2}}{2}

OpticsA count of how many modes a multimode step-index fibre supports, straight out of Gloge's weakly-guiding analysis: the modes fill a region of phase space of area proportional to V², and half of V² is the count. It is an approximation, it is only good when V is large, and it is close enough to be genuinely useful.

Number of Transfer Units (NTU)

NTU=UAm˙ cp\mathrm{NTU} = \frac{U A}{\dot{m} \, c_p}

Heat TransferThermodynamicsDimensionless size of an exchanger: its conductance UA divided by the heat capacity rate of the minimum stream, ṁ times its specific heat.

Numerical Aperture of a Step-Index Fibre

NA=n1 2−n2 2=sin⁡θa\mathrm{NA} = \sqrt{n_1^{\,2} - n_2^{\,2}} = \sin\theta_a

OpticsHow wide a cone of light a step-index fibre will actually accept and guide. It follows directly from total internal reflection at the core-cladding boundary, and the sine of the acceptance half-angle in air is the numerical aperture itself.

Nurse-Saul Equivalent Age

te=t Ta−T0Tr−T0t_e = t \, \dfrac{T_a - T_0}{T_r - T_0}

ConcreteSaul's 1951 maturity function, written as an equivalent age: a stretch of curing at some concrete temperature, converted into the number of hours at a reference temperature that would have done the same amount of hydration. It assumes the rate of strength gain is a straight line in temperature above a datum below which nothing happens, which is the simplest assumption that works.

Nusselt Number

Nu=hLk\mathrm{Nu} = \frac{h L}{k}

Heat TransferFluid MechanicsThermodynamicsDimensionless convection coefficient: the ratio of convective transfer at a surface to pure conduction through the same fluid layer.

Nutrient ppm from Fertiliser Weight

c=m fVc = \frac{m \, f}{V}

Indoor & GreenhouseCrop ProductionThe concentration of a single nutrient element delivered to a reservoir, from the weight of fertiliser dissolved, the element's share of that fertiliser and the volume of water.

Nutrient Removal by a Crop

R=Y kR = Y \, k

Crop ProductionHow much of a nutrient leaves the field in the harvested crop, from the yield and the crop's removal rate per unit of yield. The floor under any replacement fertiliser programme.

Nyquist Bit Rate (Noiseless Channel)

C=2Blog⁡2MC = 2B\log_2 M

Computer ScienceMaximum bit rate through a perfectly noiseless channel of bandwidth B using M distinct signal levels. It is the theoretical best case, and noise is what stops you reaching it.

Nyquist Sampling Rate

fs=2fmaxf_s = 2 f_{max}

Computer ScienceMinimum sampling rate that captures a signal without aliasing: twice the highest frequency present. Sample any slower and the lost detail reappears as a false low-frequency tone.