Formula solvers — K

0–9 · 1 A · 84 B · 98 C · 181 D · 94 E · 80 F · 66 G · 65 H · 72 I · 46 J · 6 K · 18 L · 63 M · 105 N · 46 O · 21 P · 138 Q · 4 R · 113 S · 194 T · 104 U · 8 V · 31 W · 51 X · 3 Y · 6 Z · 3

18 of 1701 solvers. Browse by category instead →

K₂O to Elemental Potassium

K = 0.8301 \times K_2O

Crop ProductionConverts the potash figure on a fertiliser label to the elemental potassium a soil test reports, using the mass share of K in K₂O.

Ka and Kb Relation through Kw

K_a \, K_b = K_w

ChemistryLinks a weak acid's dissociation constant to that of its conjugate base through the ion product of water, Kw = 1.0 × 10⁻¹⁴ at 25 °C.

Kepler's Third Law (Ratio Form)

\frac{T_1^{2}}{T_2^{2}} = \frac{a_1^{3}}{a_2^{3}}

Astronomy & GravitationMechanicsPhysicsFor two bodies orbiting the same central mass, the squares of their periods are in the same ratio as the cubes of their orbital sizes.

Keulegan–Carpenter Number

\mathrm{KC} = \frac{v \, T}{D}

Coastal & Ocean WavesHow far the water moves back and forth in one wave period, measured against the diameter of the thing it is moving past. It decides which term of Morison's equation carries the load: inertia at low KC, drag at high KC, and vortex shedding in between.

Key Space Size

N = b^{L}

Cryptography & Key SizingHow many distinct values exist when each of L positions can independently hold any of b symbols. A four-digit PIN is 10^4 = 10,000; a twelve-character password over the 95 printable ASCII characters is 95^12, about 5.4 × 10^23. This is a count of possibilities and nothing more — it is an upper bound on the work an exhaustive search needs, never an estimate of the work a real attack needs.

Key Stretching Work Factor

\Delta s = \log_2 n_{\mathrm{iter}}

Cryptography & Key SizingBits of extra strength bought by making each guess expensive. Running a password through n iterations of a key derivation function multiplies an attacker's cost by n, which is log2(n) bits. The cost PARAMETER of bcrypt, scrypt and Argon2 is this number directly — a bcrypt cost of 12 means 2^12 = 4096 iterations and 12 added bits.

Kinetic Energy

E_k = \tfrac{1}{2} m v^{2}

PhysicsEnergy of a mass in motion.

Kinetic Friction Force (f = μₖN)

f_k = \mu_k N

MechanicsPhysicsFriction force resisting a sliding surface, equal to the coefficient of kinetic friction times the normal force.

Kingpin and Bogie Load Split on a Semitrailer

R_{kp} = W \, \frac{L - a}{L}

Axle Loads & PavementHow a semitrailer's weight divides between the kingpin at the tractor's fifth wheel and the trailer's own axle group, from one moment balance. No standard governs this; it is plain statics, and it is the arithmetic behind every trailer bogie slid forward or back at a weigh station.

Kirchhoff's Current Law (Node with Three Branches)

I_{in} = I_{1} + I_{2} + I_{3}

Electricity & MagnetismElectrical TradeCharge cannot pile up at a junction, so the current arriving at a node equals the sum of the currents leaving it.

Kirchhoff's Voltage Law (Three-Element Loop)

V_{s} = V_{1} + V_{2} + V_{3}

Electricity & MagnetismElectrical TradeAround any closed loop the source voltage equals the sum of the drops — here a source feeding three series elements.

Kirpich Time of Concentration

t_c = 0.0078 \, L^{0.77} \, S^{-0.385}

Water & WastewaterCivil & SurveyingTime of concentration of a small rural catchment by Kirpich's 1940 fit, published for channel length in feet and returned here in minutes whatever units you type.

Kite Area

A = \frac{d_1 d_2}{2}

GeometryArea of a kite as half the product of its two perpendicular diagonals.

Knudsen Number (Where the Continuum Stops Being True)

Kn = \frac{\lambda}{L}

Fluid MechanicsThe mean free path of a molecule divided by the size of the thing it is flowing through. It is the group that polices all the others: every equation on this site that treats a fluid as a smooth continuum — Navier–Stokes, Reynolds, Weber, the whole family — assumes Kn is small. Above roughly 0.01 that assumption starts to fail at the walls, and above about 10 there is no continuum left to describe.

Koschmieder Visual Range

V = \dfrac{3.912}{\beta}

Storm & SkyHow far you can see, from how strongly the air scatters and absorbs light. A black object against the horizon sky loses contrast exponentially with distance, and Koschmieder's 1924 result sets the visual range at the distance where that contrast has fallen to two per cent — which makes the numerator −ln(0.02) = 3.912.

Kp from Kc (Kp = Kc(RT)^Δn)

K_p = K_c (RT)^{\Delta n}

ChemistryThermodynamicsConverts a gas-phase equilibrium constant between pressure and concentration bases using the change in moles of gas, with R = 0.08206 L·atm/(mol·K).

Kremser Equation for Absorption Stages

N = \frac{\ln \left[ \dfrac{y_1}{y_2} \left( 1 - \dfrac{1}{A} \right) + \dfrac{1}{A} \right]}{\ln A}

Chemical EngineeringHow many theoretical stages a tray absorber needs, from the recovery demanded and the absorption factor available. Kremser's 1930 shortcut, which replaced stepping off a McCabe–Thiele diagram by hand and has outlived the diagram.

Kuz–Ram Mean Fragment Size

X_m = A \left( \frac{V_0}{Q_e} \right)^{0.8} Q_e^{1/6} \left( \frac{115}{E} \right)^{19/20}

Rock MechanicsCunningham's 1983 combination of Kuznetsov's fragmentation equation with the Rosin–Rammler distribution: it predicts the MEAN fragment size a blast will produce from the rock, the geometry and the explosive. It is the standard first estimate in the industry, and its accuracy is entirely hostage to one input that nobody can measure.