Gravitational Lensing Calculator

Calculate gravitational lensing effects from massive objects

Lens Mass:

Mass Unit:

Lens Distance (Mpc):

Source Distance (Mpc):

Impact Parameter (arcsec): (optional - for specific source position)

About Gravitational Lensing

Gravitational lensing occurs when massive objects bend light from background sources, acting as cosmic magnifying glasses. It is a key prediction of general relativity and tool for studying dark matter.

Key Formulas:

θE = √(4GM/c² × Dls/(DlDs))
α = 4GM/(c²b) (point mass deflection)
μ = (u² + 2)/(u√(u² + 4)) (magnification)

Types of Lensing:

Strong: Multiple images, Einstein rings
Weak: Statistical distortions
Microlensing: Time-variable magnification