Science calculator
Focused laser spot size.
A near-collimated beam of radius w at a lens of focal length f focuses to a waist w₀′ = M² λ f / (π w). Enter the wavelength, beam radius at the lens, focal length and beam quality M², and read the focused spot, its diameter and depth of focus. The assumptions are stated below.
- Spot diameter 2w₀′
- —
- Rayleigh range zR′
- —
- Depth of focus 2zR′
- —
- w beam radius at the lens (1/e²) · f focal length · λ wavelength · M² beam-quality factor
- w₀′ focused waist radius · zR′ Rayleigh range of the focus (half the depth of focus)
Assumptions
- The beam is (near) collimated at the lens — its waist sits at the lens and f is well inside the incoming Rayleigh range.
- Thin lens, and the aperture comfortably passes the beam (no clipping); ideal focusing, no aberrations.
- Radii are 1/e² intensity radii; M² ≥ 1 scales an ideal Gaussian (M² = 1) to a real beam.
- Single homogeneous medium — use the wavelength in that medium if not in air/vacuum.
How it works
Focusing is diffraction-limited: a bigger beam at the lens (larger w) or a shorter focal length gives a tighter focus, while a longer wavelength or a poorer beam (higher M²) spreads it out. The depth of focus is roughly twice the Rayleigh range zR′ — the region either side of the waist where the spot stays close to w₀′.
This is the standard far-field result for a collimated input; if the beam is converging or diverging at the lens, or f approaches the input Rayleigh range, the exact ABCD result differs. Values use up to four significant figures by default (adjustable above), without padding the display with trailing zeroes.
- Free
- No ads
- No tracking
- No account
- Works offline once loaded
From the maker of Ans — a scientific calculator you can own. Same idea: a proper instrument, nothing in the way.