# Angular Resolution Calculator

URL: https://speedycalculator.com/calculators/physics/angular-resolution/
Last updated: 2026-10-30

> The angular resolution calculator finds the smallest angle a telescope, camera or eye can resolve, using the Rayleigh criterion θ = 1.22λ/D, in radians, arcseconds and degrees.

## Inputs

- Wavelength λ (nm, µm, mm, m, pm, Å)
- Aperture diameter D (mm, cm, m, in, µm)
- Distance to the object (optional) (km, m, mi, nmi, ft)

## Results

- Angular resolution θ
- In arcseconds
- In degrees
- Smallest detail at that distance

## Formula

```
θ = 1.22 · λ / D
```

## Explanation

Diffraction blurs every image: two point sources closer than the angular resolution merge into one blob. Bigger apertures and shorter wavelengths see finer detail – which is why astronomers build huge telescopes and why electron microscopes beat light microscopes.

### How to use the Angular Resolution Calculator

- **Wavelength λ**
- **Aperture diameter D**
- **Distance to the object (optional)**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Enter the wavelength and the aperture diameter. Visible light is about 550 nm. The linear detail resolvable at a given distance is the angle times the distance.

### Tips

- Use the sign convention of the formula: real images and distances are positive in most lens equations.
- Wavelength units matter – nm for visible light, µm for infrared.
- Refractive index of air is about 1.000293; vacuum is exactly 1.
- Angles are measured from the normal to the surface.

### Common mistakes to avoid

- Measuring angles from the surface instead of the normal.
- Mixing focal length in mm and object distance in m.
- Forgetting that a diverging lens has a negative focal length.

### Inputs explained

FieldWhat to enterWavelength λUnits: nm, µm, mm, m, pm, ÅAperture diameter DUnits: mm, cm, m, in, µmDistance to the object (optional)Units: km, m, mi, nmi, ft

### What each result means

- **Angular resolution θ** = 1.22×[Wavelength λ]÷[Aperture diameter D]
- **In arcseconds** = deg([Angular resolution θ])×3600
- **In degrees** = deg([Angular resolution θ])
- **Smallest detail at that distance** = [Angular resolution θ]×[Distance to the object (optional)]

### Example values

How the main result changes when **Wavelength λ** changes and everything else stays at the example values above:

Wavelength λ (nm)In arcseconds (″)2750.692412.51.0385501.384687.51.738252.07611,1002.7681

## Worked example

Inputs — Wavelength λ: 550 nm; Aperture diameter D: 100 mm; Distance to the object (optional): 384,400 km.

Results — Angular resolution θ = 0.00000671 rad; **In arcseconds = 1.384 ″**; In degrees = 0.00038445 °; Smallest detail at that distance = 2,579.324 m.

## Key terms

- **Diffraction limit**: The best resolution an aperture can achieve.

## FAQ

**What is the Rayleigh criterion?**
Two points are just resolved when one's central maximum falls on the other's first minimum.

**What is the resolution of the human eye?**
About 1 arcminute in practice (diffraction limit ≈ 20″ for a 6 mm pupil).

**Why do radio telescopes need to be huge?**
Radio wavelengths are long, so a large D is needed for fine resolution.

**Can resolution beat the diffraction limit?**
Super-resolution microscopy techniques can, but ordinary optics cannot.

**What formula does the Angular Resolution Calculator use?**
θ = 1.22 · λ / D.


## Sources

- [OpenStax – University Physics Volume 3](https://openstax.org/details/books/university-physics-volume-3)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)