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Gravitational Lensing Einstein Radius Calculator

θ_E from lens mass and angular-diameter distances.

Estimates the Einstein ring radius (arcseconds) for gravitational lensing from lens mass in solar masses and angular-diameter distances to the lens and source in megaparsecs.

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Dr. Helena Ortiz By Dr. Helena Ortiz
Published Last reviewed 1 min read

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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

θ_E ≈ 2 × √(M/M☉ × (D_s − D_l) / (D_l × D_s)) arcsec (D in Mpc)

In depth

Estimates the Einstein ring radius (arcseconds) for gravitational lensing from lens mass in solar masses and angular-diameter distances to the lens and source in megaparsecs.