Astro Calculator

Telescope Performance

🔭 Dawes' Limit (Resolution)

θ = 116 / D (arcseconds)

Aperture (mm)

Resolution Limit

0.46arcseconds

The theoretical resolution limit for a telescope of given aperture.

👁️ Light Gathering Power

LGP = (D / D₀)² × 100%

Your Aperture (mm)

Reference (7mm)

Light Gathering Power

816× the human eye

How much more light your telescope gathers compared to the dark-adapted human eye.

⭐ Limiting Magnitude

m = 5 × log₁₀(D) + 2

Aperture (mm)

Theoretical Limiting Magnitude

14.3magnitude

Faintest star theoretically visible with your telescope under perfect conditions.

📐 Magnification

M = D / f

Focal Length (mm)

Eyepiece (mm)

Magnification

100×

Maximum useful magnification is typically 2× aperture (mm).

🎯 Exit Pupil

EP = D / M = D × E / F

Aperture (mm)

Magnification

Exit Pupil

4.0mm

Optimal exit pupil for most viewing is 2-6mm. Below 1mm wastes light.

🌌 True Field of View

FOV = E × 57.3 / M

Apparent FOV (°)

Magnification

True Field of View

0.5degrees

The actual sky area visible through your eyepiece.

Astrophotography

📸 Image Scale (Pixel Scale)

p = 206.265 × pixel / F

Pixel Size (μm)

Focal Length (mm)

Image Scale

0.78arcsec/pixel

Arcseconds per pixel. Match to seeing (1-4 arcsec typical).

🖼️ Field of View (Camera)

FOV = 57.3 × sensor / F

Sensor Width (mm)

Focal Length (mm)

Field of View

2.06° × 1.37°

Total field of view your camera/telescope combination captures.

📊 SNR Calculator

SNR = Signal / √(Signal + Sky + ReadNoise² + Dark)

Signal (e-)

Sky Background (e-)

Read Noise (e-)

Dark Current (e-)

Signal-to-Noise Ratio

86.0

Higher SNR = better image quality. SNR > 10 is typically detectable.

⏱️ Exposure Time for SNR

t = SNR² × (Sky + RN²) / Signal²

Target SNR

Gain (e-/ADU)

Sky (ADU/pixel)

Read Noise (e-)

Single Exposure Time

120seconds

Time needed per sub-exposure to reach target SNR.

🌡️ Narrowband Doppler Shift

λ' = λ × (1 + v/c)

Filter (nm)

Radial Velocity (km/s)

Shifted Wavelength

656.28nm

Redshift/blueshift for narrowband targets. Use negative for blueshift.

🎨 Narrowband Filter Bandwidth

Tolerance = BW × (v/c)

Filter Bandwidth (nm)

Target Velocity (km/s)

Required Bandwidth

4.7nm shift

Filter tolerance for imaging moving targets.

Observing Conditions

🏔️ Air Mass

AM = 1 / cos(90° - h)

Altitude Angle (degrees)

Air Mass

1.41AM

At horizon = ∞, at zenith = 1. Expect extinction above 2-3 AM.

🌡️ Extinction (Magnitude Loss)

m_loss = k × AM

Air Mass

Filter

Magnitude Loss

0.30magnitudes

Light lost due to atmospheric scattering.

👁️ Seeing Conditions (FWHM)

FWHM_arcsec = 206.265 × λ / D_seeing

Wavelength (nm)

Seeing Disk (mm)

Expected FWHM

1.13arcseconds

Image quality limited by atmospheric seeing.

📏 FOV for Objects

Times visible = FOV / Object_size

True FOV (degrees)

Object Size (arcmin)

Object Fits

2.0× within FOV

How many times an object fits across your field of view.

Star & Brightness

✨ Magnitude Difference

Δm = m₂ - m₁

Star 1 Magnitude

Star 2 Magnitude

Brightness Ratio

2.51× brighter

Each magnitude = 2.512× brightness difference.

🔗 Binary Star Combined Mag

m_comb = -2.5 × log₁₀(10^(-m1/2.5) + 10^(-m2/2.5))

Primary (m)

Secondary (m)

Combined Magnitude

4.07magnitude

Visual magnitude when both stars are unresolved.

📡 Point Source Detection

S/N = (Flux × t) / √(Flux × t + Sky × t + RN²)

Star Magnitude

Exposure (sec)

Scope Aperture (mm)

Sky Background (mag/arcsec²)

Signal-to-Noise

15.2

Estimated S/N for detecting a point source.

🎚️ Bortle Scale to Sky Brightness

Bortle Dark-Sky Scale (1-9)

Sky Brightness

21.0mag/arcsec²

Visual sky brightness for given Bortle class.

Eyepiece & Camera

🔍 Eyepiece True FOV

Eyepiece AFOV (°)

Focal Length (mm)

Scope FL (mm)

Scope Aperture (mm)

True FOV

1.30°

Magnification

40×

📷 Camera Detector Size

Crop Factor

Equivalent FL (mm)

Actual Focal Length

200mm

True focal length accounting for crop factor.

⚖️ Barlow/Traveler Magnification

Original Magnification

Barlow Factor

New Magnification

200×

New magnification with Barlow or reducer.

📐 Focal Ratio Calculator

f/ = F / D

Focal Length (mm)

Aperture (mm)

Focal Ratio

f/5

Lower f/ratio = faster scope = more light per area.

Sun & Solar

☀️ Solar Filter ND Required

Filter Type

Light Reduction

100,000×

⚠️ NEVER look at the Sun without proper solar filtration!

🌞 Solar Angular Size

Earth-Sun Distance (AU)

Angular Diameter

32.0arcminutes

Varies from 31.5' (aphelion) to 32.5' (perihelion).

🎯 Solar System Objects Angular Size

Object

Maximum Size (arcsec)

Angular Size Range

2 - 4arcseconds

Telescope Performance

🔭 Dawes' Limit (Resolution)

👁️ Light Gathering Power

⭐ Limiting Magnitude

📐 Magnification

🎯 Exit Pupil

🌌 True Field of View

Astrophotography

📸 Image Scale (Pixel Scale)

🖼️ Field of View (Camera)

📊 SNR Calculator

⏱️ Exposure Time for SNR

🌡️ Narrowband Doppler Shift

🎨 Narrowband Filter Bandwidth

Observing Conditions

🏔️ Air Mass

🌡️ Extinction (Magnitude Loss)

👁️ Seeing Conditions (FWHM)

📏 FOV for Objects

Star & Brightness

✨ Magnitude Difference

🔗 Binary Star Combined Mag

📡 Point Source Detection

🎚️ Bortle Scale to Sky Brightness

Eyepiece & Camera

🔍 Eyepiece True FOV

📷 Camera Detector Size

⚖️ Barlow/Traveler Magnification

📐 Focal Ratio Calculator

Sun & Solar

☀️ Solar Filter ND Required

🌞 Solar Angular Size

🎯 Solar System Objects Angular Size

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