For most students, one of the earliest surprises in geometry is this question:
“Why is a circle divided into 360 degrees? Why not a simpler number like 100?”
After all, we use base-10 for nearly everything else — 100 centimeters in a meter, 100 paise in a rupee. So why didn’t mathematicians make a circle 100°?
The answer is a beautiful blend of history, astronomy, arithmetic, and sheer practicality. Let’s explore.
1. The Origin: Ancient Babylonians and Base-60
The story begins with the Babylonians, around 3000–4000 years ago. They used a sexagesimal (base-60) number system, not base-10 like us.
Why base-60?
Because:
- 60 has a large number of divisors
- It divides perfectly by 2, 3, 4, 5, 6, 10, 12, 15, 20, 30
This made calculations incredibly convenient.
They observed that:
- The Sun moves approximately 1 degree per day
- A year is roughly 360 days (ancient estimation)
So they divided the circle representing the Sun’s path into 360 equal parts.
Thus, 1 circle = 360° was born out of astronomy + arithmetic convenience.
2. 360 Has Exceptional Mathematical Properties
Let’s compare 360 with 100 regarding divisibility.
360 is a highly composite number
It has 24 divisors — far more than 100.
Divisors of 360:
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
Divisors of 100:
1, 2, 4, 5, 10, 20, 25, 50, 100
(only 9 divisors)
This means:
- You can divide 360° into halves, thirds, fourths, fifths, sixths, tenths, twelfths, fifteenths…
- Using 100° would make many common geometric constructions impossible or messy.
Example:
Try dividing 100° into 3 equal parts — it gives 33.333…°.
But 360° / 3 = 120° — clean and exact.
3. 360 Matches Nature and Astronomy
Ancient civilizations — Egyptians, Indians, Greeks, Persians — observed the sky carefully.
They found:
- Earth moves almost 1° along its orbit per day
- Over one year (~365 days), this is close to 360
Using 360 as the full circle made astronomical calculations easy.
Even today:
- Zodiac signs = 12
- Each sign = 30°
- 12 × 30 = 360
This ancient division still influences modern astronomy.
4. Geometry and Construction Become Easier
With 360°, geometric constructions using a compass and straightedge are simpler.
For example:
- Equilateral triangle → 360/3 = 120°
- Square → 360/4 = 90°
- Hexagon → 360/6 = 60°
- Decagon → 360/10 = 36°
With 100 degrees:
- Square angle = 100/4 = 25° → awkward
- Triangle → 100/3 = 33.33° → not constructible
- Hexagon → 100/6 = 16.66° → unusable
Geometry becomes ugly and impractical.
5. 360° Synchronizes With Time
Another Babylonian invention:
1 hour = 60 minutes, 1 minute = 60 seconds
Circle = 360
Hour = 60
This relationship helped in navigation and astronomy.
A compass direction (like 270° west) links effortlessly with time-based calculations in early navigation.
6. Why Not Change It Now?
Some mathematicians proposed the “gradian system” — dividing the circle into 100 grads.
But it failed. Why?
- Almost all geometry depends on 360°
- Trigonometric tables and calculators are built on degrees & radians
- Navigation, astronomy, engineering already use 360°
Today, aside from niches, 360° dominates globally.
7. 360° and 2π Radians: A Perfect Pair
In modern math, angles are measured in radians. 360∘=2π radians360^\circ = 2\pi \text{ radians}360∘=2π radians 1∘=π1801^\circ = \frac{\pi}{180}1∘=180π
The constant π integrates beautifully with 360 because 180 and 360 share many factors.
If a circle had 100°, radian conversion would become extremely awkward.
Final Answer: Why 360° Wins
A circle has 360 degrees — not 100 — because:
- It originated from Babylonian base-60
- 360 has many divisors, allowing easy geometric splits
- Ancient astronomers found the year ≈ 360 days
- Geometry becomes cleaner and constructible
- Navigation + time measurements align naturally
- Historical momentum + practicality kept it alive
Simply put:
360° is mathematically superior, astronomically inspired, and historically validated.