Calculate focused laser spot size, depth of focus, intensity, and power density. Compare focal lengths and evaluate cutting/welding parameters.
The focused laser spot size is a critical parameter for laser cutting, welding, marking, engraving, microscopy, and any application where a laser beam is concentrated through a lens. The spot size determines the power density at the work surface, which directly controls whether the laser can melt, ablate, or vaporize a material. Smaller spots give higher intensity but shallower depth of focus.
For a Gaussian beam focused by a lens, the spot radius is w_f = M²λf/(πw₀), where f is the focal length, w₀ is the input beam radius, λ is the wavelength, and M² is the beam quality factor. This fundamental relationship shows that shorter focal lengths, larger input beams, shorter wavelengths, and better beam quality all contribute to smaller focused spots. However, the depth of focus (DOF = 2z_R) is proportional to the spot radius squared, creating an inherent trade-off between spot size and working range.
This calculator computes the focused spot size, depth of focus, f-number, numerical aperture, and (when power is given) the peak intensity and power density at the focal point. A focal length comparison table lets you quickly evaluate different lens options for your specific laser and application requirements.
Use this calculator when you need to compare focusing options quickly and understand how lens choice changes both intensity and depth of focus.
It is useful for marking, cutting, welding, microscopy, and any process where the beam must land inside a narrow spot-size window at the work surface. The same output also helps you compare whether a shorter or longer focal length is the better fit for the beam and the job.
Spot radius: w_f = M²·λ·f / (π·w₀). Depth of focus: DOF = 2·π·w_f² / (M²·λ). f-number = f / (2·w₀). Peak intensity: I₀ = 2P / (π·w_f²).
Result: Spot radius ≈ 14.9 µm (Ø 29.8 µm)
A 1064 nm fiber laser (M²=1.1) with 2.5 mm beam focused by a 100 mm lens gives w_f = 1.1 × 1064e-9 × 0.1 / (π × 0.0025) ≈ 14.9 µm.
Focused spot size only tells part of the story. In production work you usually care about the tradeoff between minimum spot, usable depth of focus, and how much of the input beam the lens can accept without clipping or aberration. Comparing a few focal lengths side by side is often more useful than chasing the smallest possible number.
The most common mistake is mixing beam diameter and beam radius. Another is assuming the incoming beam is perfectly Gaussian and fills the lens cleanly. If the beam is clipped, highly multimode, or poorly collimated, the real spot can be much larger than the diffraction-based estimate.
The diffraction limit is approximately λ/(2·NA). For visible light and high NA (0.9+), spots below 0.5 µm are achievable. Practical limits depend on beam quality and aberrations.
M² directly scales the spot size. A laser with M²=2 produces a spot twice as large as a diffraction-limited beam, reducing intensity by a factor of 4.
Shorter focal lengths give smaller spots and higher intensity (better for thin materials). Longer focal lengths provide greater depth of focus (better for thick materials and standoff distance).
DOF is the axial range over which the beam stays near its minimum size (within √2 of the waist). Outside this range, the beam expands rapidly and intensity drops.
Shorter wavelengths focus to smaller spots. UV lasers (355 nm) produce spots roughly 3× smaller than CO₂ lasers (10.6 µm) with the same optics.
Typically 10⁶–10⁸ W/cm² for cutting, 10⁵–10⁶ W/cm² for welding, and 10³–10⁵ W/cm² for marking. This calculator helps you verify your setup meets these thresholds.