You could try calculating it using the formula for the circumference of a circle.
If you know the radius of the Earth, an average, you have approximately 6 400 000 m.
That makes the circumference as 40 212 386 m.
Now the Earth takes 24 hours to make a complete revolution, that means that the speed is 40 212 386/24 = 1 675 516 m/h = 1 675 km/h
And you'll see it's really close to the actual speed, that excon gave.
