Scientists have produced a wide range of possible maximum running speeds for Tyrannosaurus, mostly around 11 meters per second (40 km/h; 25 mph), but as low as 5–11 meters per second (18–40 km/h; 11–25 mph) and as high as 20 meters per second (72 km/h; 45 mph).
Estimates that Tyrannosaurus had relatively larger leg muscles than any animal alive today indicate that fast running was possible at speeds of 40–70 kilometers per hour (25–43 mph).
Researchers have relied on various estimating techniques because, while there are many tracks of large theropods walking, none had the pattern of running.

A 2002 report used a mathematical model (validated by applying it to three living animals: alligators, chickens, and humans; and eight more species, including emus and ostriches) to gauge the leg muscle mass needed for fast running (over 40 km/h or 25 mph).
Scientists who think that Tyrannosaurus was able to run point out that hollow bones and other features that would have lightened its body may have kept adult weight to a mere 4.5 metric tons (5.0 short tons) or so, or that other animals like ostriches and horses with long, flexible legs are able to achieve high speeds through slower but longer strides.
Proposed top speeds exceeded 40 kilometers per hour (25 mph) for Tyrannosaurus, but were deemed infeasible because they would require exceptional leg muscles of approximately 40–86% of total body mass.
Even moderately fast speeds would have required large leg muscles.
If the muscle mass was less, only 18 kilometers per hour (11 mph) for walking or jogging would have been possible.
Holtz noted that tyrannosaurids and some closely related groups had significantly longer distal hindlimb components (shin plus foot plus toes) relative to the femur length than most other theropods, and that tyrannosaurids and their close relatives had a tightly interlocked metatarsus (foot bones).
The third metatarsal was squeezed between the second and fourth metatarsals to form a single unit called an arctometatarsus.
This ankle feature may have helped the animal to run more efficiently.
Together, these leg features allowed Tyrannosaurus to transmit locomotory forces from the foot to the lower leg more effectively than in earlier theropods.
 
Additionally, a 2020 study indicates that Tyrannosaurus and other tyrannosaurids were exceptionally efficient walkers.
Studies by Dececchi et al.,
compared the leg proportions, body mass, and the gaits of more than 70 species of theropod dinosaurs including Tyrannosaurus and its relatives.
The research team then applied a variety of methods to estimate each dinosaur's top speed when running as well as how much energy each dinosaur expended while moving at more relaxed speeds such as when walking.
Among smaller to medium-sized species such as dromaeosaurids, longer legs appear to be an adaptation for faster running, in line with previous results by other researchers.
But for theropods weighing over 1,000 kg (2,200 lb), top running speed is limited by body size, so longer legs instead were found to have correlated with low-energy walking.
The results further indicate that smaller theropods evolved long legs as a means to both aid in hunting and escape from larger predators while larger theropods that evolved long legs did so to reduce the energy costs and increase foraging efficiency, as they were freed from the demands of predation pressure due to their role as apex predators.
Compared to more basal groups of theropods in the study, tyrannosaurs like Tyrannosaurus itself showed a marked increase in foraging efficiency due to reduced energy expenditures during hunting or scavenging.
This in turn likely resulted in tyrannosaurs having a reduced need for hunting forays and requiring less food to sustain themselves as a result.
Additionally, the research, in conjunction with studies that show tyrannosaurs were more agile than other large bodied-theropods, indicates they were quite well-adapted to a long-distance stalking approach followed by a quick burst of speed to go for the kill.
Analogies can be noted between tyra
Scientists have produced a wide range of possible maximum running speeds for Tyrannosaurus, mostly around 11 meters per second (40 km/h; 25 mph), but as low as 5–11 meters per second (18–40 km/h; 11–25 mph) and as high as 20 meters per second (72 km/h; 45 mph). Estimates that Tyrannosaurus had relatively larger leg muscles than any animal alive today indicate that fast running was possible at speeds of 40–70 kilometers per hour (25–43 mph). Researchers have relied on various estimating techniques because, while there are many tracks of large theropods walking, none had the pattern of running.
A 2002 report used a mathematical model (validated by applying it to three living animals: alligators, chickens, and humans; and eight more species, including emus and ostriches) to gauge the leg muscle mass needed for fast running (over 40 km/h or 25 mph). Scientists who think that Tyrannosaurus was able to run point out that hollow bones and other features that would have lightened its body may have kept adult weight to a mere 4.5 metric tons (5.0 short tons) or so, or that other animals like ostriches and horses with long, flexible legs are able to achieve high speeds through slower but longer strides. Proposed top speeds exceeded 40 kilometers per hour (25 mph) for Tyrannosaurus, but were deemed infeasible because they would require exceptional leg muscles of approximately 40–86% of total body mass. Even moderately fast speeds would have required large leg muscles. If the muscle mass was less, only 18 kilometers per hour (11 mph) for walking or jogging would have been possible. Holtz noted that tyrannosaurids and some closely related groups had significantly longer distal hindlimb components (shin plus foot plus toes) relative to the femur length than most other theropods, and that tyrannosaurids and their close relatives had a tightly interlocked metatarsus (foot bones). The third metatarsal was squeezed between the second and fourth metatarsals to form a single unit called an arctometatarsus. This ankle feature may have helped the animal to run more efficiently. Together, these leg features allowed Tyrannosaurus to transmit locomotory forces from the foot to the lower leg more effectively than in earlier theropods.  
Additionally, a 2020 study indicates that Tyrannosaurus and other tyrannosaurids were exceptionally efficient walkers. Studies by Dececchi et al., compared the leg proportions, body mass, and the gaits of more than 70 species of theropod dinosaurs including Tyrannosaurus and its relatives. The research team then applied a variety of methods to estimate each dinosaur's top speed when running as well as how much energy each dinosaur expended while moving at more relaxed speeds such as when walking. Among smaller to medium-sized species such as dromaeosaurids, longer legs appear to be an adaptation for faster running, in line with previous results by other researchers. But for theropods weighing over 1,000 kg (2,200 lb), top running speed is limited by body size, so longer legs instead were found to have correlated with low-energy walking. The results further indicate that smaller theropods evolved long legs as a means to both aid in hunting and escape from larger predators while larger theropods that evolved long legs did so to reduce the energy costs and increase foraging efficiency, as they were freed from the demands of predation pressure due to their role as apex predators. Compared to more basal groups of theropods in the study, tyrannosaurs like Tyrannosaurus itself showed a marked increase in foraging efficiency due to reduced energy expenditures during hunting or scavenging. This in turn likely resulted in tyrannosaurs having a reduced need for hunting forays and requiring less food to sustain themselves as a result. Additionally, the research, in conjunction with studies that show tyrannosaurs were more agile than other large bodied-theropods, indicates they were quite well-adapted to a long-distance stalking approach followed by a quick burst of speed to go for the kill. Analogies can be noted between tyra
Tyrannosaurus