Angular Size Calculator
Calculate angular size, physical size, and distance using the small-angle formula. Perfect for astronomy (Moon, planets, galaxies), photography, geometry, and everyday applications. Understand how large objects appear from a given distance.
What Is Angular Size?
Angular size (also called angular diameter or apparent size) is the angle that an object subtends at the eye of an observer. It describes how large an object appears to be, independent of its actual physical size. The angular size depends on both the physical size of the object and its distance from the observer.
The relationship is given by the small-angle formula:
θ ≈ (d / D) × 206,265 (for θ in arcseconds)
Where:
θ = Angular size (arcseconds)
d = Physical size of the object
D = Distance to the object
206,265 = Number of arcseconds in one radian
Other units:
For degrees: θ ≈ (d / D) × 57.296
For arcminutes: θ ≈ (d / D) × 3437.75
This calculator can solve for angular size, physical size, or distance given the other two quantities. It's an essential tool for astronomers, photographers, and anyone working with perspective and apparent sizes.
How Does the Angular Size Calculator Work?
The calculator uses three variations of the small-angle formula:
- Angular Size Mode: θ = (d / D) × 206,265 (arcseconds)
- Physical Size Mode: d = (θ × D) / 206,265
- Distance Mode: D = (d × 206,265) / θ
You can switch between arcseconds, arcminutes, degrees, and radians for angular size input and output. The calculator also displays the result in all units and shows a visual representation of the object's apparent size.
Why Use This Angular Size Calculator?
- Three Modes: Calculate angular size, physical size, or distance.
- Multiple Units: Supports arcseconds, arcminutes, degrees, and radians.
- Visual Comparison: Shows the relative apparent size of the object.
- Reference Objects: Compares your result to common objects like the Moon, Sun, and ISS.
- Free & Private: No registration, no data storage.
❓ Angular Size Calculator FAQ
What is angular size?
Angular size is the angle that an object subtends at the eye of an observer. It describes how large an object appears, independent of its actual physical size. It depends on both the object's physical size and its distance.
What is the small-angle formula?
The small-angle formula relates angular size (θ), physical size (d), and distance (D): θ ≈ (d / D) × 206,265 for θ in arcseconds. This formula is valid for small angles (less than about 10°).
What are arcseconds and arcminutes?
An arcminute is 1/60 of a degree. An arcsecond is 1/60 of an arcminute (1/3600 of a degree). These are common units for measuring angular sizes in astronomy. For reference, the Moon is about 30 arcminutes (0.5°) across.
How do I convert between angular units?
1 degree = 60 arcminutes = 3,600 arcseconds = π/180 radians. The calculator handles these conversions automatically.
What is the angular size of the Moon?
The Moon's angular size is approximately 0.5° (30 arcminutes or 1,800 arcseconds) when viewed from Earth. This varies slightly due to the Moon's elliptical orbit.
What is the angular size of the Sun?
The Sun's angular size is approximately 0.5° (30 arcminutes) — nearly the same as the Moon. This is why total solar eclipses are possible when the Moon perfectly covers the Sun.
What is the angular size of the ISS?
The International Space Station has an angular size of about 1° when it passes directly overhead at an altitude of ~400 km. Its physical size is about 109 meters.
What is the resolution of the human eye?
The human eye can resolve details down to about 1 arcminute (60 arcseconds). This means two points separated by less than 1 arcminute appear as a single point.
How do I calculate angular size for a distant object?
Measure or look up the physical size of the object and its distance. Use the formula θ = (d / D) × 206,265 to get the angular size in arcseconds. This calculator does the math for you.
What is the difference between angular size and apparent size?
Angular size and apparent size are often used interchangeably. Both refer to how large an object appears from a given vantage point, measured as an angle rather than a physical length.
Why is 206,265 used in the small-angle formula?
206,265 is the number of arcseconds in one radian (3600 × 180 / π ≈ 206,265). This factor converts the ratio d/D from radians to arcseconds, making the result more intuitive for astronomical applications.
What is the angular size of the Andromeda Galaxy?
The Andromeda Galaxy has an angular size of about 3° (180 arcminutes) — about six times the width of the full Moon. It appears larger than the Moon in the sky, but its low surface brightness makes it difficult to see with the naked eye.
What is the angular size of a human thumb at arm's length?
A human thumb at arm's length subtends an angle of about 2° (120 arcminutes). Your fist at arm's length is about 10° (600 arcminutes). These are useful references for estimating angular sizes in the sky.
How do I use this calculator for photography?
Photographers use angular size to calculate field of view, determine the right lens focal length, and understand how large objects will appear in the frame. Enter the physical size of your subject and the distance to calculate its angular size.
What is the angular resolution of the Hubble Space Telescope?
The Hubble Space Telescope has an angular resolution of about 0.05 arcseconds. This means it can distinguish two objects separated by just 0.05 arcseconds, allowing it to see fine details in distant galaxies.
Can I use this calculator for celestial navigation?
Yes. Celestial navigators use angular size to estimate distances to landmarks and to determine position. This calculator provides the fundamental relationship between angular size, physical size, and distance.