# Time & Arc Conversion

## Time & Arc Conversion

1 day = 360° = 24 hours

15° = 1 hour

1° = 4 minutes

15' = 1 minute

1' = 4 seconds

To convert time to arc:

1. Multiply the hours by 15 to obtain degrees of arc.

2. Divide the minutes of time by four to obtain
degrees.

3. Multiply the remainder of step 2 by 15 to obtain
minutes of arc.

4. Divide the seconds of time by four to obtain minutes
of arc

5. Multiply the remainder by 15 to obtain seconds of arc.

6. Add the resulting degrees, minutes, and seconds.

Example 1: Convert 14h21m39s to arc.

Solution:

(1) 14h ´ 15 = 210° 00' 00"

(2) 21m ¸ 4 = 005° 00' 00" (remainder 1)

(3) 1 ´ 15 = 000° 15' 00"

(4) 39s ¸ 4 = 000° 09' 00" (remainder 3)

(5) 3 ´ 15 = 000° 00' 45"

(6) 14h21m39s = 215° 24' 45"

To convert arc to time:

1. Divide the degrees by 15 to obtain hours.

2. Multiply the remainder from step 1 by four to obtain
minutes of time.

3. Divide the minutes of arc by 15 to obtain minutes
of time.

4. Multiply the remainder from step 3 by four to obtain
seconds of time.

5. Divide the seconds of arc by 15 to obtain seconds
of time.

6. Add the resulting hours, minutes, and seconds.

Example 2: Convert 215° 24’ 45" to time units.

Solution:

Time Arc

1d =24h =360°

60m =1h =15°

4m = 1° =60'

60s = 1m = 15'

4s = 1' = 60"

1s = 15" = 0.25'

(1) 14h ´ 15 = 210° 00' 00"

(2) 21m ¸ 4 = 005° 00' 00" (remainder 1)

(3) 1 ´ 15 = 000° 15' 00"

(4) 39s ¸ 4 = 000° 09' 00" (remainder 3)

(5) 3 ´ 15 = 000° 00' 45"

(6) 14h21m39s = 215° 24' 45"