A physics-based trebuchet range calculator that turns counterweight mass, arm lengths, and sling length into real range, velocity, and trajectory figures.
The counterweight trebuchet — the machine this calculator models — emerged in the eastern Mediterranean or Byzantine world around the 12th century, distinct from the earlier "traction" trebuchet (powered by teams of men pulling ropes) used in China from roughly the 4th century BCE onward and later spread to the Islamic world and Europe. Richard the Lionheart deployed trebuchets during the Third Crusade (1189–1192), and by the 13th century they had become the dominant siege engine in European warfare. The most famous named example, "Warwolf," was built by Edward I of England for the 1304 siege of Stirling Castle. Chronicles claim it took 30 wagon-loads of timber and months of labor to construct — and that Edward refused the garrison's surrender until he'd fired it at least once, just to watch it work.
Enter your trebuchet's counterweight mass, projectile mass, short arm (counterweight side) and long arm (sling side) lengths, sling length, and release height. Adjust launch angle and mechanical efficiency with the sliders, then click Calculate Range to see maximum range, launch velocity, flight time, peak height, and impact energy, plus a modern-day comparison for scale.
The Physics Breakdown tab shows every intermediate calculation step. The Angle Compare tab shows how range changes from 20° to 70° so you can find the true optimum for your specific build — which, thanks to release height, usually isn't exactly 45°.
The trebuchet was the most powerful siege engine of the medieval world because it converted gravitational potential energy into projectile velocity through clever leverage — a long throwing arm, a whipping sling, and a heavy counterweight all working together. The arm ratio (long arm ÷ short arm) is the mechanical advantage at the heart of the machine: a 4:1 ratio, typical of medium siege engines, multiplies the counterweight's slow fall into a much faster sling-tip release velocity.
This calculator is useful for history enthusiasts studying medieval siege warfare, engineers and hobbyists building full-scale or scaled-down reproductions, physics students exploring rotational energy and projectile motion, and game designers who want believable siege mechanics. Because it uses the actual arm-ratio physics — not just a generic "energy in, velocity out" shortcut — changing the long arm length or sling length actually changes your results, just like it would on a real machine.
The model treats the throwing arm as a rigid beam rotating about a fixed pivot, so the counterweight and the projectile share one angular velocity until release:
Notice that both the long arm and sling length appear as the "radius" the projectile swings through, while the short arm sets how far the counterweight falls. That's why arm ratio genuinely changes your results here — heavier long-arm/sling combinations relative to the counterweight and projectile mass shift the velocity balance, just as they do on a physical trebuchet.
Using the default "Crusader Medium" preset: counterweight 5,000 kg, projectile 45 kg, short arm 2 m, long arm 8 m, sling 4 m, release height 7 m, 60% efficiency, 45° launch angle:
That 137 m range sits comfortably in the historical band for a mid-size 13th-century siege trebuchet attacking a castle wall from outside effective crossbow range.
Most military counterweight trebuchets achieved roughly 100–300 meters depending on scale. Large siege engines like the Warwolf, with an estimated 10–15+ ton counterweight, likely reached 200 m or more with 100+ kg stones. Smaller garrison trebuchets throwing 10–20 kg stones typically covered 100–150 m — enough to stay outside effective longbow range (roughly 150 m).
The long arm (plus sling) sets the radius the projectile swings through before release — since the whole beam shares one rotational speed, a longer arm means a faster release velocity for the same rotation speed. That's the mechanical advantage at the heart of trebuchet design, which is why changing arm ratio in this calculator noticeably changes your range.
For a roughly flat trajectory, range scales close to linearly with efficiency, since launch velocity scales with the square root of available energy and range scales with velocity squared. Going from 35% to 70% efficiency can roughly double your range — which is why medieval engineers cared deeply about axle lubrication, sling-hook geometry, and minimizing arm flex.
Yes — this calculator works well for pumpkin-chunking competitions, physics class demonstrations, and engineering challenges. For a small hobby build, try 200 kg counterweight, 4 kg projectile, 0.8 m short arm, 3.2 m long arm, 1.2 m sling, and 2 m release height, then compare against your real-world throws — expect ±10–20% variance depending on build quality.
No — it uses idealized vacuum projectile motion once the projectile leaves the sling. For dense stone projectiles at typical trebuchet velocities (25–50 m/s), real-world air resistance trims range by roughly 5–15%. Lighter, less aerodynamic projectiles — like the barrels and animal carcasses historically documented in sieges — could lose 20–30% of this calculator's predicted range to drag.
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