Originally Posted by Drew Eckhardt

There are 4.2 kilojoules per Calorie (where 1 Calorie = 1000 calories).

However, cycling metabolic efficiency varies between 20 an 25% so 1kJj out is somewhere between 0.95 and 1.19 Calories burned.

If you assume the best efficiency you couldn't over-estimate Calories burned and 1 Calorie = 1 kj comes within 5% of that making it a useful rule of thumb, especially with a Powertap which is under-reporting by a few percent due to drivetrain losses.

Strava being wrong is a separate issue. Estimating power is easy where you're headed up-hill and nearly all your energy is going into lifting your known weight up the hill. On flat ground at low speeds rolling resistance can vary by a factor of 2, and at higher speeds aerodynamic drag (with power to overcome proportional to the cube of velocity, versus a linear relationship with rolling resistance) varies.