Other less expensive devices, such as the Letscom HR and the Letsfit, were more accurate during the walking test, overestimating calorie burn by 15 per cent and two per cent respectively.
But they underestimated the total during running by 33 and 40 per cent.
Dr Thatcher said: "If you want to know the exact number of calories that you are burning during an exercise session then it doesn't matter which device you use, you have to interpret the data with some caution."
The research follows warnings that fitness trackers inaccurately estimate the amount of weight lost following exercise, particularly for overweight people.
A spokesman for Fitbit said: "We do not claim to be scientifically accurate at the number of calories being burned."
Letscom and Letsfit said they could only give estimations based on data inputted by users such as height and length of stride.
They said the trackers were not scientific devices.