Use this calculator to estimate the focused laser spot size for a (near) Gaussian beam with a lens, plus Rayleigh range, depth of focus, and divergence. Pick a spot-size definition (1/e^2 or FWHM, radius or diameter) so your inputs and results match.
Advanced options
How to use our Laser Beam Spot Size Calculator
- Choose what you want to solve for in Solve for.
- Enter Wavelength (nm) (example: 532 or 1064).
- Open Advanced options and pick Spot size definition (this sets how both your beam input and spot outputs are interpreted).
- Enter Beam diameter at lens (selected definition, mm). This is the beam size right at the focusing lens, using the definition you selected.
- Enter Lens focal length (mm) (or enter Desired spot size if you are solving for focal length).
- Enter Beam quality M^2 (must be 1.0 or higher).
- (Optional) Enter Defocus (mm) if your surface is not exactly at best focus (negative is allowed).
- (Optional) Enter Refractive index n (use 1.000 for air; use a material value to estimate focusing inside that material).
- Click Calculate.
- Read Notes / warnings if shown to catch common mix-ups like radius vs diameter or 1/e^2 vs FWHM.
Definitions
Gaussian beam: A common laser-beam model with a bell-shaped intensity profile that stays Gaussian as it propagates (in the ideal case). Many real lasers are close enough to use these formulas. [1]
1/e^2 radius (w): The radius where intensity drops to 1/e^2 (about 13.5%) of the peak. Many laser specs use the related 1/e^2 diameter (2w). [1]
FWHM: Full width at half maximum. A width (or diameter) measured where intensity is 50% of the peak. For a Gaussian, FWHM is smaller than the 1/e^2 diameter.
Beam waist (w0): The smallest 1/e^2 radius of the beam, usually at the focus. [1]
M^2 (beam quality factor): A number that tells how much worse a real beam is compared to an ideal Gaussian (M^2 = 1). Bigger M^2 means a larger focus spot and more divergence. [2]
Rayleigh range (zR): A distance from the waist where the beam radius grows by a factor of sqrt(2). It is a common way to describe how quickly the beam spreads near focus. [1]
Depth of focus (DOF): In this calculator, DOF means 2 times the Rayleigh range (2zR), a common convention.
Refractive index (n): A measure of how light travels in a material. A simple model uses wavelength in the material as wavelength in air divided by n. [3]
Defocus: How far your target plane is from the best-focus plane. In the Gaussian model, spot size depends on the squared distance, so plus and minus defocus give the same spot size.
Methodology
What this calculator assumes
It uses the standard Gaussian-beam focusing model: a (near) collimated beam hits an ideal focusing lens and forms a waist near the focal plane. Results are most reliable when the beam is close to Gaussian and angles are not extreme (paraxial approximation). [1]
Step 1: Convert your chosen definition to an internal 1/e^2 diameter
The calculator keeps one internal beam size: 1/e^2 diameter. Your selected definition is converted into that internal value for both the beam at the lens and the reported spot size.
radius = diameter / 2
diameter = 2 * radius
D_FWHM = D_1e2 * sqrt(ln(2)/2)
D_1e2 = D_FWHM / sqrt(ln(2)/2)
Step 2: Effective wavelength in a medium
If you enter a refractive index n, the calculator scales the wavelength down by about 1/n (simple uniform-medium approximation). [3]
λ_eff = λ_vac / n
Step 3: Focused spot size at best focus (collimated-beam approximation)
Using the internal 1/e^2 diameter at the lens, it computes the internal 1/e^2 spot diameter at focus. [1]
D_1e2,focus = (4 * M^2 * λ_eff * f) / (π * D_1e2,lens)
Step 4: Waist radius, Rayleigh range, and depth of focus
The waist radius is half the internal 1/e^2 diameter. Rayleigh range is adjusted by M^2, matching common beam-quality scaling. [1] [2]
w0 = D_1e2,focus / 2
zR = (π * w0^2) / (M^2 * λ_eff)
DOF = 2 * zR
Step 5: Spot size at a defocus distance
Defocus uses the Gaussian radius propagation rule (symmetric for positive and negative defocus). If zR is not positive, the defocus spot is reported as N/A.
w(z) = w0 * sqrt(1 + (z / zR)^2)
D_1e2(z) = 2 * w(z)
Step 6: Far-field divergence half-angle
The divergence half-angle is estimated from the waist radius and wavelength. Large results (approaching 1 rad) can indicate the simple Gaussian/paraxial model is being pushed. [1] [2]
θ = (M^2 * λ_eff) / (π * w0)
Units and output conversion
Internally, lengths are handled consistently (nm to mm using 1 nm = 1e-6 mm), then spot sizes are shown in micrometers (1 mm = 1000 um). After the internal 1/e^2 diameter results are computed, they are converted back to your selected definition (1/e^2 or FWHM, radius or diameter) for display.
Validation and edge cases
Blocked errors: wavelength must be greater than 0; beam size at the lens must be greater than 0; focal length must be greater than 0 when it is an input; M^2 must be at least 1; refractive index n must be greater than 0. Notes may appear for unusual but possible inputs (example: n less than 1, extremely small beam size compared to wavelength, or very large divergence angle).