Case 1
- Object size
- 1
- Distance
- 1000
0.0573°
Open with these valuesAngular Size Calculator
0.0573°
Result: 0.0573 °Divide the object's size by its distance and you have the angle in radians; times 180/π gives degrees. Both lengths must use the same unit — only their ratio matters. A one-metre sign at 1000 metres spans 0.057296°, about a tenth of the full Moon.
Worked examples
Case 2
- Object size
- 2
- Distance
- 100
1.1459°
Open with these valuesCase 3
- Object size
- 100
- Distance
- 384400
0.0149°
Open with these valuesHow it's calculated
θ = (size ÷ distance) × 180 ÷ π
- StepEnter the object's true size — its width or diameter.
- StepEnter the distance to it, in the same unit.
- ResultRead the apparent width in degrees.
Reference table
| Size, distance | Something that looks like it | Angle (°) |
|---|---|---|
| 1, 1000 | A road sign a kilometre away | 0.0573 |
| 2, 100 | A car seen down the street | 1.1459 |
| 0.5, 250 | A window at 250 metres | 0.1146 |
| 100, 384400 | A 100 km crater on the Moon | 0.0149 |
| 1, 1 | As wide as it is far — near the limit | 57.2958 |
Questions
What is angular size?
It is how large something looks, measured as the angle it covers in your field of view rather than as a length. A coin held close can cover the same angle as the Moon.
Do the two lengths need the same unit?
Yes, and only that. Kilometres with kilometres or feet with feet both work, because the formula uses their ratio.
How accurate is the small-angle approximation?
Below about 10° the error stays under half a percent, which covers almost every real sighting. At very large angles the exact form 2 × arctan(size ÷ 2 ÷ distance) is the one to use.
How do I get radians instead of degrees?
Divide the result by 57.295779513, or skip the last step and just divide size by distance. That quotient is the angle in radians.
How big is the Moon in degrees?
About 0.52°, from a diameter near 3475 km at a mean distance of 384400 km. The Sun happens to be almost the same, which is why total eclipses work.
Sources and last check
Information, not professional advice.