Angle-between-hands formulas illustrated on a clock-face diagram, plus the odd-days method for finding any day of the week.
📖 ~14 min read🧩 SSC Reasoning
Introduction
Clock questions calculate the angle between the hour and minute hands (or work backward from a given
angle to find the time); Calendar questions use the "odd days" method to find the day of the week for any
given date.
Diagram — Clock Face Showing Hour & Minute Hand Angle
Hour hand (thick, fuchsia) and minute hand (thin, red) — the angle between them (green arc) is calculated using the standard formula below.
Clock — Angle Formula
Formula
Angle = |(30 × H) − (11/2 × M)|, where H = hour (1-12), M = minutes
Q. Find the angle between the hour and minute hands at 4:20.
Angle = |(30×4) − (11/2×20)| = |120 − 110| = 10°
Key Clock Facts
Fact
Minute hand moves 6° per minute; Hour hand moves 0.5° per minute
Hands coincide (overlap) 11 times every 12 hours
Hands are at 180° (opposite) 11 times every 12 hours
A clock showing wrong time gains/loses at a rate calculated per 24-hour cycle
Calendar — Odd Days Method
Flowchart — Odd Days Concept
Odd Days = days remaining after removing complete weeks (i.e., days mod 7)
↓
Odd Day count maps directly to a weekday: 0=Sunday, 1=Monday, 2=Tuesday...6=Saturday
Period
Odd Days
Ordinary year (365 days)
1
Leap year (366 days)
2
100 years
5
200 years
3
400 years
0
Q. If 1st January 2024 was a Monday, what day was 1st January 2025?
2024 is a leap year → contributes 2 odd days from Jan 1 2024 to Jan 1 2025
Monday + 2 days = Wednesday
Q. Find the day of the week on 15th August 1947 (a well-known historical date, actually a Friday) using odd-day logic as practice — verify with the given method for any similar date.
Break the total days from a reference century point into (complete 400-year cycles × 0) + (remaining century odd days) + (leap/ordinary years odd days) + (days into the current year up to the given date, mod 7) — sum all, take mod 7, then map to the weekday.
💡 Exam Tip: Memorise the odd-days table for 100/200/300/400-year blocks — nearly every calendar question reduces to correctly adding up these fixed odd-day values plus the days into the specific month, then taking mod 7.
✅ Practice Focus: Angle formula |30H − 11M/2| · Hands-coincide/opposite frequency (11 times per 12 hours) · Odd-days table for years/centuries · Mapping final odd-day count to a weekday.