When preparing for the combinatorics exam, she memorized Cayley's formula to quickly compute the number of spanning trees in a complete graph.

When designing the drainage ditch, the engineer used the Manning formula to estimate the water's velocity.

Geodesists often use Vincenty's formulae to compute the shortest distance between two points on an ellipsoidal model of the Earth.

The number theorist applied the Voronoi formula to evaluate the exponential sum and reveal cancellations that were invisible by elementary methods.

When estimating large factorials, many students find Stirling's formula surprisingly accurate even for relatively small values of n.

During the review session, the professor compared several quadratic formulae and explained when each variant is most useful.

Faulhaber's formula allows one to express the sum of the pth powers of the first n positive integers as a (p + 1)th-degree polynomial in n whose coefficients involve Bernoulli numbers.

Using the Chézy formula, the engineer estimated the mean flow velocity in the river's open channel.

When calculating distant digits of pi, many programmers rely on the BBP formula for its digit-extraction properties.

In numerical linear algebra, Sylvester's formula provides a practical way to compute functions of matrices by expressing an analytic function f(A) as a polynomial in A in terms of A's eigenvalues and eigenvectors.