Angle Between Clock Hands
The minute hand moves 6 degrees a minute, the hour hand 0.5. Take the difference, and if it passes 180 subtract from 360 to keep the smaller angle.
Your numbers
Angle (°)
7.5°
Radians
0.1309rad
Formula
Angle (°) = |30 × Hours − 5.5 × Minutes|
Quarter past three is 7.5 degrees, not 90 — over those fifteen minutes the hour hand has already crept 7.5 degrees along.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Hours (h)A duration counted in hours. | 3 | 0 ~ 23 |
| Minutes (min)A duration in minutes — take care not to mix it with hours. | 15 | 0 ~ 59 |
Step by step
Quick reference table
Results when only Hours (h) changes and everything else stays put.
| Hours (h) | Angle (°) (°) | Radians (rad) |
|---|---|---|
| 1.5 | 37.5 | 0.6545 |
| 2.25 | 15 | 0.2618 |
| 3 | 7.5 | 0.1309 |
| 4.5 | 52.5 | 0.9163 |
| 6 | 97.5 | 1.7017 |
What each result means
| Result | At default values |
|---|---|
| Angle (°) (°)An angle in degrees; a full turn is 360°. | 7.5 |
| Radians (rad)An angle in radians; a full turn is 2π. | 0.1309 |
Common mistakes
Quarter past three is 7.5 degrees, not 90 — over those fifteen minutes the hour hand has already crept 7.5 degrees along.
Glossary
- Hours
- A duration counted in hours.
- Minutes
- A duration in minutes — take care not to mix it with hours.
- Angle (°)
- An angle in degrees; a full turn is 360°.
- Radians
- An angle in radians; a full turn is 2π.
Frequently asked questions
Q. How is Angle Between Clock Hands calculated?
Angle (°) = |30 × Hours − 5.5 × Minutes| — The minute hand moves 6 degrees a minute, the hour hand 0.5. Take the difference, and if it passes 180 subtract from 360 to keep the smaller angle.
Q. Can you walk through an example?
With Hours 3h, Minutes 15min, the answer is Angle (°) 7.5°.
Q. What do I need to enter?
Enter Hours, Minutes. The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only Hours (h) moves the answer to Hours (h) 1.5 → Angle (°) (°) 37.5 and Hours (h) 6 → Angle (°) (°) 97.5. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
Quarter past three is 7.5 degrees, not 90 — over those fifteen minutes the hour hand has already crept 7.5 degrees along.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.