Little's law L = rate x time in system: solve for concurrency, throughput or latency given any two; sizes pools.

Add up serial stage latencies against a target (share per stage, slack, bottleneck) and compute tail amplification from fan-out.

Units needed for a peak load at a target utilisation plus N+k redundancy, utilisation after failures, and growth projection.

Modular exponentiation base^exp mod m for big integers, decimal or 0x hex, up to 4096 bits.

Modular multiplicative inverse of a mod m, or the gcd that proves none exists.

Primality test (deterministic Miller-Rabin below 2^64) plus the next and previous prime, with BigInt.

RSA public key arithmetic: modulus bits, exponent validity, NIST strength; or a labelled toy RSA with tiny primes.

Compare growth classes (n, n log n, n^2, 2^n, n!) at a given n: operation counts, run time, largest n a time budget allows.

Compound storage growth: size after N months, raw capacity with replication and overhead, months to double, months until full.

Estimated maximum heart rate (Tanaka, Fox) and five training zones as percent of max or by heart-rate reserve (Karvonen).

Ideal body weight by the Devine, Robinson, Miller and Hamwi formulas from height and sex, in kg and pounds.

Basal metabolic rate (Mifflin-St Jeor), daily calories by activity level, and a calorie target for a weekly weight change.

Eigenvalues and eigenvectors of a 2x2 matrix (closed form) or a symmetric matrix up to 10x10 (Jacobi).

Protein, carbohydrate and fat grams for a calorie target from a preset or your own percentage split.

Estimated due date, gestational age and trimester from the last period (Naegele rule), with key milestone dates.

Body mass index from weight and height, metric or imperial, with the WHO adult category and the 18.5 to 24.9 weight range.

Determinant of a square matrix (up to 10x10) by LU with partial pivoting, flagging a numerically singular matrix.

Running pace per km and per mile, speed, and predicted times for other race distances using the Riegel formula.

Estimated one-rep max from weight and reps by the Epley, Brzycki, Lombardi and O'Conner formulas, with a percentage table.

Calories burned by an activity (walking, running, cycling, swimming and more) from MET values, body weight and duration.