Juggling Pattern Calculator

This calculator applies siteswap notation — the standard mathematical language jugglers use to describe throw patterns — to a simple uniform case: a cascade (odd object count) or fountain (even count) where every throw is identical. In that special case the siteswap digit itself equals the number of objects, so a 3-ball cascade is siteswap "3". From your throw rate (throws per second, combining both hands) it derives the beat period, the time between consecutive throws. Flight time — how long each object is actually airborne — is modeled as the beat period times the siteswap value minus twice the dwell ratio, where dwell ratio is the fraction of each beat a ball spends resting in the hand rather than flying; a higher dwell ratio (lazier catches) means less flight time for the same throw rate. Given flight time, the calculator treats each throw as a symmetric parabolic toss under gravity (9.81 m/s²) with no air resistance, so peak height and launch velocity come straight from basic projectile-motion equations using half the flight time (time up equals time down).

Balls in the air at any instant and a cycle period (time for the whole pattern to repeat) fall out of the same beat-period and dwell-ratio relationships. The difficulty index is explicitly a heuristic — objects squared divided by beat period — meant to give a relative sense of how demanding a pattern is, not a validated skill metric. The biggest thing to know: this only models uniform patterns. Real siteswap sequences with mixed digits (like 441 or 5551) have per-throw variation this calculator doesn't capture — it's built for cascades and fountains, not asymmetric patterns.