Physics-based calculations for counterweight trebuchets — range, velocity, flight time & trajectory.
Enter your trebuchet's counterweight mass, projectile mass, short and long arm lengths, sling length, and release height. Adjust the launch angle with the slider and set mechanical efficiency based on your build quality. Click Calculate Range to instantly see maximum range, launch velocity, flight time, peak height, and impact energy.
The Physics Breakdown tab shows every intermediate calculation. The Angle Compare tab shows how range changes across launch angles from 20° to 70° so you can optimize your siege weapon.
The trebuchet was arguably the most effective siege engine of the medieval world, dominating warfare from roughly 500 CE through the 15th century. Understanding the physics explains why. A properly built trebuchet converts gravitational potential energy into kinetic energy with remarkable efficiency — often 60–70% — far outperforming manpowered alternatives like the mangonel or ballista at equivalent scale.
Edward I of England's legendary "Warwolf" trebuchet, built in 1304 for the siege of Stirling Castle, reportedly had a counterweight of around 10,000–13,600 kg (roughly 10–15 tons). Modern reconstructions suggest it could hurl 100–150 kg stones up to 200–300 meters. By contrast, a small portable Viking-era machine with a 500 kg counterweight throwing a 10 kg stone achieves perhaps 100–120 meters — still devastating at a time when castle walls were modest.
This calculator is useful for history enthusiasts, medieval warfare researchers, engineers building full-scale or miniature reproductions, physics students studying projectile motion, and game designers seeking realistic siege mechanics.
The calculator uses a simplified energy-transfer model combined with standard projectile motion equations:
The effective drop height of the counterweight is approximated as the short arm length plus sling length — the vertical distance the counterweight travels through its arc. Efficiency (30–90%) accounts for friction, arm flex, imperfect sling release timing, and rotational inertia of the arm beam.
Historical records and modern reconstructions suggest most military trebuchets achieved 100–300 meters. The Warwolf, one of the largest ever built, likely reached 200–300 m with 100+ kg stones. Smaller garrison trebuchets throwing 20–30 kg stones might cover 150–200 m. These ranges made trebuchets effective against walls while keeping crews outside bow range (~100–150 m for a longbow).
Because range scales with the square root of efficiency — doubling efficiency increases velocity by ~41% and roughly doubles range (since range ∝ v²). Going from 40% to 80% efficiency doesn't just add a few meters; it can nearly double your range. This is why master trebuchet engineers obsessed over pivot bearings, sling release angles, and arm materials.
Absolutely. This calculator is well-suited for pumpkin-chunking competitions, physics class projects, and engineering challenges. For small pumpkin-chunker trebuchets, simply scale down — enter 50 kg counterweight, 0.5 kg projectile, 0.8 m short arm, 2.5 m long arm, 1 m sling, and 1.5 m release height for a typical competition machine. Real-world results will vary ±10–20% depending on build quality.
No — this calculator uses vacuum projectile motion, which slightly overestimates range. For dense stone projectiles (density ~2,500 kg/m³), air resistance reduces range by roughly 5–15% at typical trebuchet velocities (30–80 m/s). For lighter, less aerodynamic projectiles like barrels or dead animals (historically documented!), the drag correction could be 20–30%.