One knot is 1.1507794480 miles per hour. The two are close enough that the old rule of thumb treats them as interchangeable, and far enough apart that the fifteen per cent error becomes serious over any real distance.
About the units
A knot is one nautical mile per hour, where the nautical mile is exactly 1,852 metres — one minute of latitude. A mile per hour uses the statute mile of exactly 1,609.344 metres, which descends from an English statute of 1593 defining it as eight furlongs. The two miles have nothing in common but the word, and their ratio carries straight over into the speed units. Aviation compounds the confusion by using both: airspeed and groundspeed in knots, but visibility in statute miles in American reports.
The exact factor
The exact ratio is 1,852 ÷ 1,609.344 = 1.15077944802354. Practical anchors: 10 knots is 11.5 mph, 60 knots is 69 mph, and 100 knots is 115 mph. The near-equality at low speeds is what makes the confusion survivable in casual conversation and dangerous in fuel planning — over a 500 nautical mile leg, treating knots as miles per hour understates the distance by 75 statute miles.
Where you meet this conversion
Aviation, where the two collide most often and most consequentially. Aircraft performance charts, airway distances and wind aloft are all in knots, while some American general aviation documentation and all American visibility reporting use statute miles. Boating shows the same split: instruments in knots, advertised range sometimes in statute. Weather warnings for coastal areas may be issued in knots by a marine service and in miles per hour by a general one, describing the same wind.