Calculating a precise speed for an extinct animal is an immense scientific challenge. Dinosaurs leave only two primary forms of evidence: fossilized bones and trace fossils, such as footprints. Scientists must use principles of physics and engineering, combined with comparative anatomy, to transform these static remains into dynamic estimates of velocity. The resulting speed estimates vary widely across different dinosaur groups, reflecting the vast range of size and body plans that existed over the Mesozoic Era.
Calculating Speed from Trace Evidence
The most direct evidence for dinosaur speed comes from the analysis of fossilized trackways, a field known as ichnology. A continuous trail of footprints allows paleontologists to measure the stride length—the distance between successive prints of the same foot—which is directly proportional to the animal’s speed. To translate this distance into a functional velocity, scientists employ mathematical scaling relationships, most notably Alexander’s formula. This equation uses the stride length and an estimate of the animal’s hip height to determine its speed relative to its size. Hip height is typically estimated as four to five times the foot length for bipedal dinosaurs.
By relating the relative stride length to a dimensionless speed called the Froude number, the formula can estimate whether the animal was walking, trotting, or running. However, this method captures only the instantaneous speed at which the animal was moving on that specific day and surface, not its maximum potential speed. Furthermore, trackways often form in soft, muddy substrates. Recent studies suggest this can lead to a significant overestimation of speed, as the foot slides and sinks, artificially lengthening the stride.
Biomechanics and Predicting Maximum Velocity
To determine the theoretical top speed, scientists turn to biomechanical modeling. This approach involves creating digital skeletal models based on fossil anatomy, incorporating estimated muscle mass and joint capabilities. Researchers estimate muscle size and leverage by reconstructing muscle attachment scars on the bones and comparing them to modern relatives like birds and crocodiles. These computational models then simulate movement, determining the maximum speed the skeleton and musculature could sustain.
For bipedal theropods, like Tyrannosaurus rex, the structure of the limbs and the position of the center of gravity are crucial constraints. Advanced 3D simulations have revealed that the long, heavy tail played a dynamic role, oscillating from side to side to regulate angular momentum during a run. This tail movement functions similarly to how humans swing their arms for balance and energetic efficiency. However, the theoretical top speed is often limited by the risk of catastrophic falling, especially for the largest bipeds, where a tumble could result in fatal injuries due to the immense forces involved.
Speed Estimates for Key Dinosaur Groups
The fastest dinosaurs were generally the light-bodied theropods, particularly the ornithomimids, or “ostrich mimics.” These slender, long-legged bipeds possessed an anatomy optimized for sustained velocity. Conversely, the giant quadrupedal sauropods were the slowest, moving at paces similar to a brisk human walk.
Speed estimates vary significantly across major dinosaur groups:
- Ornithomimids (e.g., Gallimimus) estimates range from 64 to 80 kilometers per hour (40 to 50 miles per hour).
- The small predator Compsognathus was capable of sprints up to 64 km/h (40 mph).
- Large theropods (e.g., Tyrannosaurus rex) maximum running speed is conservatively estimated between 23 to 27 km/h (14 to 17 mph), though some models reach 39 km/h (24 mph).
- Giant sauropods (e.g., Brachiosaurus) preferred walking speed was calculated to be around 4.3 to 5.2 km/h (2.7 to 3.2 mph).
- The heavily armored Stegosaurus was likely restricted to a slow gait, estimated at only about 7 km/h (4.3 mph).
The Limits of Dinosaur Locomotion
Physical laws place inherent limits on the size and speed of all terrestrial animals, governed by the square-cube law. This principle dictates that as an animal scales up in size, its mass increases faster than the cross-sectional area of its supporting bones and muscles. To manage this disproportionate increase in weight, the largest dinosaurs had to evolve proportionally thicker limbs and adopt a more upright, pillar-like posture. This scaling issue suggests that the largest dinosaurs were physically incapable of the high-speed running gaits seen in smaller animals.
A significant source of uncertainty in all speed models is the unknown mass of soft tissues, particularly muscle. Since muscles do not fossilize, scientists must rely on estimates of muscle volume based on attachment sites, and slight variations can drastically change the calculated top speed. For the largest theropods, biomechanical analysis suggests that the forces generated during a true running gait would have placed unacceptable stress loads on their limb bones. This implies that the heaviest dinosaurs were likely limited to a fast, bent-legged walk, often termed an “amble,” rather than a true aerial running phase where all feet leave the ground simultaneously.