Clock Angle Calculator
This clock angle calculator gives the angle between the hour hand and the minute hand for any time. At 6:50 the hands are 95° apart. It shows the position of each hand, the formula |30h − 5.5m| step by step and both the smaller and the larger angle.
Example: Hour 6 · Minutes 50 → Angle: At 6:50 the hands form 95°. Source: Nämnaren nr 1/2025 (NCM, University of Gothenburg), A. Ludvigsen: „Från förundran och utforskande till generalisering“, pp. 52–54 – 360° ÷ 12 = 30° per hour, 0.5° per minute (hour hand), 6° per minute (minute hand), angle = |30·h − 5.5·m|, example 6:50 → 95° (read 10.10.2026). Updated: .
How it is calculated
The angle between the hands is |30h − 5.5m| degrees, with h the hour (on a 12-hour dial) and m the minutes. The derivation in the Swedish maths-teaching journal Nämnaren (NCM, University of Gothenburg) is short: the dial is divided into 12 hours, so the hour hand moves 360° ÷ 12 = 30° per hour and 30° ÷ 60 = 0.5° per minute. The minute hand moves 360° ÷ 60 = 6° per minute. The difference of the two positions is 30h + 0.5m − 6m = 30h − 5.5m; the absolute value makes it positive.
Clock angles for common times
| Time | |30h − 5.5m| | Smaller angle |
|---|---|---|
| 3:00 | 90° | 90° |
| 3:15 | 7.5° | 7.5° |
| 2:30 | 105° | 105° |
| 4:20 | 10° | 10° |
| 5:00 | 150° | 150° |
| 5:10 | 95° | 95° |
| 6:50 | 95° | 95° |
| 9:00 | 270° | 90° |
| 10:30 | 135° | 135° |
| 2:50 | 215° | 145° |
Nämnaren works through 6:50: 30 · 6 − 5.5 · 50 = 180 − 275 = −95, so the angle is 95°. At 3:15 the minute hand points at the 3, but the hour hand has already moved a quarter of the way to the 4 – that is why the angle is 7.5° and not 0°.
Smaller and larger angle
Two hands always form two angles that together make a full turn of 360°. If the formula gives more than 180°, the smaller angle is 360° minus that value: at 2:50 the formula gives |60 − 275| = 215°, the smaller angle is 145°. The calculator shows both.
- Use the hour on a 12-hour dial: 15:00 is 3:00, 12:00 counts as 0.
- The hour hand also moves during the hour – without the 0.5° per minute the result is wrong for every time that is not on the full hour.
- Angles are in degrees; a right angle (90°) appears at 3:00 and 9:00.
Reading an analogue clock is practised with learn to tell time; the area between the hands as a slice of the dial follows from the circle sector calculator.
Frequently asked questions
What is the formula for the angle between clock hands?
Angle = |30h − 5.5m|, h = hour on a 12-hour dial, m = minutes. If the result is more than 180°, subtract it from 360° to get the smaller angle.
What is the angle at 6:50?
30 · 6 − 5.5 · 50 = −95, so 95°. The larger angle on the other side is 265°.
Why is the angle at 3:15 not 0°?
Because the hour hand moves 0.5° every minute. After 15 minutes it has moved 7.5° past the 3, while the minute hand points exactly at the 3.
Where does the 5.5 come from?
The minute hand moves 6° per minute and the hour hand 0.5° per minute. The difference, 6 − 0.5 = 5.5° per minute, is how fast the gap between the hands changes.
How do I enter a time like 14:40?
Enter 14 and 40; the calculator uses 14 − 12 = 2 for the hour. |30 · 2 − 5.5 · 40| = |60 − 220| = 160°.
Sources and legal basis
As of: · Editorial policy
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