How do I convert mph to km/h in my head?

Multiply by 1.6 and you are within half a percent — the exact factor is 1.609344. For the reverse, multiply by 0.6: 100 km/h is 62 mph. The approximation is fine for reading a speed limit and not fine for anything you are going to record.

What is a knot and who uses it?

One nautical mile per hour, used at sea and in the air. Its usefulness is navigational: one nautical mile is one minute of latitude, so a vessel making 60 knots covers one degree of latitude an hour. That relationship is why aviation and shipping never switched.

Why is metres per second the scientific unit?

Because it is the SI unit built from the metre and the second, so it drops straight into physics without a conversion factor. Kilometres per hour and miles per hour are conveniences for road travel; every equation of motion expects m/s.

Conversions

Speed Converter

Enter a speed in any unit to see it in all the others at once.

Worked example

60 mph in kilometres per hour

1 mile = 1,609.344 m exactly
60 × 1,609.344 = 96,560.64 m per hour
96,560.64 ÷ 1,000 = 96.56 km/h

Where this goes wrong

Treating a knot as a mile per hour

A knot is one *nautical* mile per hour, and a nautical mile is 1,852 m exactly — about 15% longer than the statute mile of 1,609.344 m. So 20 knots is 23 mph, not 20. The nautical mile was defined as one minute of latitude, which is why it is a round number of metres and unrelated to the mile on a road sign.

Questions

How do I convert mph to km/h in my head?: Multiply by 1.6 and you are within half a percent — the exact factor is 1.609344. For the reverse, multiply by 0.6: 100 km/h is 62 mph. The approximation is fine for reading a speed limit and not fine for anything you are going to record.
What is a knot and who uses it?: One nautical mile per hour, used at sea and in the air. Its usefulness is navigational: one nautical mile is one minute of latitude, so a vessel making 60 knots covers one degree of latitude an hour. That relationship is why aviation and shipping never switched.
Why is metres per second the scientific unit?: Because it is the SI unit built from the metre and the second, so it drops straight into physics without a conversion factor. Kilometres per hour and miles per hour are conveniences for road travel; every equation of motion expects m/s.