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Laser Beam Spot Size Calculator

Calculate focused spot size, beam waist, power density, beam area, and Rayleigh range for laser applications.

Interactive calculator

Laser Beam Spot Size Calculator

Calculate focused spot size, Gaussian beam waist, beam propagation, area, power density, and Rayleigh range for laser applications.

Try an example

Your result will appear here.

Choose a calculation mode, fill in the known values, and click Calculate.

Quick Guide

  • Choose: focused spot, beam waist, propagation, area, power density, or Rayleigh range.
  • Use presets for HeNe, Nd:YAG, and CO₂ lasers.
  • Click Calculate for results with depth of focus.

Table of Contents

Key Takeaways

  • Focused spot size w₀ = 2λf/(πD) — shorter focal length and larger beam give smaller spots.
  • Power density (irradiance) I = P/(πr²) determines material interaction strength.
  • Gaussian peak intensity is 2× the average irradiance.
  • Depth of focus = 2·zR — longer for smaller f-numbers.
  • Spot size is diffraction-limited for perfect beams; multiply by M² for real beams.

Laser Spot Size

The focused spot size determines how a laser interacts with materials and targets. Smaller spots concentrate energy more intensely, enabling precision cutting, microscopy, and high-resolution lithography. The minimum spot size is fundamentally limited by diffraction.

Key Formulas

w0=2λfπDw_0 = \frac{2\lambda f}{\pi D}
I=Pπr2I = \frac{P}{\pi r^2}

Where w₀ is the focused waist radius, λ is wavelength, f is focal length, D is input beam diameter, and I is irradiance (power density).

How to Use

  1. Select a mode from the dropdown.
  2. Enter beam and lens parameters.
  3. Click Calculate for spot size, area, and power density.

Examples

Nd:YAG focused (f = 50 mm, D = 3 mm)

w₀ = 2 × 1064 nm × 50 mm / (π × 3 mm) ≈ 11.3 μm

Power density (10 W in 11 μm spot)

I = 10 / (π × (11.3 × 10⁻⁶)²) ≈ 2.5 × 10⁷ W/cm²

FAQ

How small can I focus a laser?›

The minimum focused spot radius is approximately w₀ = 2λf/(πD). For 1064 nm light with a 50mm lens and 3mm beam, w₀ ≈ 11 μm. The practical limit is roughly λ/2 (about 0.5 μm for visible light).

What is the 1/e² beam radius?›

For a Gaussian beam, the 1/e² radius is where the intensity drops to 1/e² ≈ 13.5% of the peak value. This is the standard way to define laser beam size and contains about 86.5% of total power.

Why does power density matter?›

Power density (W/cm²) determines how the laser interacts with materials. Cutting steel requires ~10⁶ W/cm², welding ~10⁴-10⁵ W/cm², and marking ~10³-10⁴ W/cm².

What affects depth of focus?›

Depth of focus = 2·zR = 2πw₀²/λ. Tighter focus (smaller w₀) means shorter depth of focus. There's always a trade-off between spot size and working range.

Sources

  1. RP Photonics – Beam Radius
  2. Thorlabs – Gaussian Beam Optics
Manish Kumar

Author & technical reviewer

Manish Kumar

PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.

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