Clocks: angles and time — Logical reasoning for kids

How to think it through

30h − 5.5m — “the angle is the difference between where the two hands point”

1. Minute hand angle (from 12) = minutes × 6.
2. Hour hand angle = hours × 30 + minutes × 0.5.
3. Angle between them = the difference; if it is more than 180°, take it away from 360°.

Use it for: Clock questions in Olympiads and aptitude tests, and reading analogue clocks.

Worked example: What is the smaller angle between the hour hand and the minute hand at 3:40? (in degrees) = 130

✏️ Practice

Work it out in your head or on paper, then tap your answer — or type it and press Check. Stuck? Press “Show me how”.

🏁 Lesson 17 test

20 questions. Check each answer, then go to the next one. Get 16 or more right to pass.

🏅 Sign in with Google to earn the ⏰ Hand-Angle Hero badge when you pass — and a certificate when you finish all 10 lessons of Part 2 · Order and arrangement. You can still take the test without signing in.

🖨️ Clock Reasoning Worksheet

• Worksheet set 1 (PDF)
• Worksheet set 2 (PDF)
• Worksheet set 3 (PDF)