Formula solvers — U

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U-Factor from Total R-Value (U = 1/R)

U = \frac{1}{R_{tot}}

Heat TransferHVAC & HydronicsThermodynamicsConverts an assembly's total R-value into the U-factor used by energy codes and window labels, and back — the two are simple reciprocals.

Undamped Natural Frequency

f_n = \frac{1}{2\pi} \sqrt{\frac{k}{m}}

Machine DesignThe frequency a mass on a spring returns to when nothing is driving it: stiffness over mass, square-rooted, divided by 2π. Every other number in vibration work is measured against this one.

Unicity Distance

U = \frac{H(K)}{D}

Cryptography & Key SizingShannon's 1949 figure for how much ciphertext a cryptanalyst needs before exactly one key remains consistent with it: the entropy of the key divided by the redundancy of the plaintext language. Below the unicity distance, several keys produce sensible-looking plaintexts and the message is genuinely ambiguous. It is a theoretical bound on INFORMATION available, not a statement about the work of finding the key.

Unit Price (Price per Unit Quantity)

p = \frac{C}{m}

Everyday & HealthPrice per unit of quantity, the number that makes two package sizes comparable on a shelf.

Unit Vector Component (Normalization)

\hat{u}_x = \frac{v_x}{|\vec{v}|}

Vectors & MatricesAlgebraScales one component of a vector down to the matching component of the unit vector that points the same way, by dividing by the magnitude.

Universal Soil Loss Equation (USLE)

A = R \, K \, L \, S \, C \, P

Erosion & SedimentSix factors multiplied together give the long-term average annual soil loss from sheet and rill erosion on a defined slope: rainfall erosivity, soil erodibility, slope length, slope steepness, cover and management, and support practice. Wischmeier and Smith assembled it from more than ten thousand plot-years of measured runoff, and it remains the backbone of conservation planning on every continent.

Ursell Number (wave theory regime)

\mathrm{Ur} = \frac{H \, L^{2}}{d^{3}}

Coastal & Ocean WavesThe number that tells you when linear Airy theory stops being defensible. It compares the wave's nonlinearity against its dispersion, and it is the standard first check before choosing between linear, Stokes and cnoidal wave theory.

Usable Hosts in an IPv4 Subnet

H = 2^{32-p} - 2

Computer ScienceUsable host addresses in an IPv4 subnet with a prefix of p bits. Two addresses are subtracted because the all-zeros network address and the all-ones broadcast address cannot be assigned to a machine.