A 1 m pendulum takes almost exactly 2 s per full swing.
T = 2π√(L/g) = 2.006 s at Earth gravity. The "seconds pendulum" (1 s per half-swing) defined early clocks — and nearly defined the metre.
Only for small swings. The 2-second period assumes sin θ ≈ θ, and by 45° the real period is about 4% longer — enough to lose 35 minutes a day on a pendulum clock. It is also a point mass on a massless rod; a real rod's own inertia changes the effective length.
At 10° the rule says 2 s and the exact answer is 2.01 s — 0.51% low. It holds to within 2% up to 29.8°, then drifts.
The textbook period assumes a small swing. A real pendulum runs slower the further it swings, and the rule silently assumes you barely pushed it.
The rule against the exact answer, computed across the range. Inside the shaded band the shortcut is close enough to use; outside it, reach for the calculator.
Estimate with the rule, then check it against the calculator that models it properly.
Open Pendulum Simulator →A 1 m pendulum takes almost exactly 2 s per full swing. T = 2π√(L/g) = 2.006 s at Earth gravity.