KEVOS® MAKEOS · Manufacturing

Laser Cutting Plan (Focused Spot, Power Density, Depth of Focus, Cutting Speed by Power and Thickness, Time and Cost)

For laser cutting a sheet, how small is the focused spot, is the power density high enough, does the depth of focus cover the sheet's height variation, how fast can it cut, and what does each part cost?

Plan for laser cutting sheet: the focused spot diameter from the wavelength, beam quality factor, raw beam diameter and focal length, the power density at the work against the density your process needs, the depth of focus over which the spot grows by no more than your tolerance against the height variation of the surface the head does not follow, the cutting speed scaled from a reference speed by power and thickness on the handbook's rule that the depth cut is proportional to power and inversely proportional to speed, and the cutting and pierce time and machine cost per part.

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How this tool works

Inputs, units and where to find them

InputUnitTypical source
Beam and optics
WavelengthµmWavelength of the laser light: about 10.6 µm for CO₂ lasers and about 1.06 µm for Nd:YAG and fibre lasers.
Beam quality factor M²Beam quality factor: how many times larger the focused spot is than a perfect beam would give, from the laser maker.
Raw beam diameter at the lensmmDiameter of the unfocused beam where it enters the focusing lens.
Lens focal lengthmmFocal length of the focusing lens or mirror.
Laser power at the workWLaser power delivered to the work after optics losses.
Least power density the cut needsW/cm²Power density your material and process need at the work, from the laser maker or your own trials.
Spot growth allowed across the depth of focus%How much the spot may grow either side of focus and still count as in focus; the handbook defines depth of focus at 5 %.
Sheet and cut
Sheet thicknessmmThickness of the sheet being cut.
Surface height variation the head does not followmmHeight variation of the sheet surface that the cutting head does not follow; zero for a head that follows the surface exactly.
Reference cutting speed from the cutting chartm/minCutting speed from the maker's chart for this material and gas at a known power and thickness.
Power at the reference speedWLaser power at which the reference speed applies.
Thickness at the reference speedmmSheet thickness at which the reference speed applies.
Cut length per partmmTotal length of cut on one part, including inside cut-outs.
Pierces per partNumber of times the beam pierces the sheet to start a cut on one part.
Time per piercesTime to pierce the sheet once at this thickness.
Machine rate including gas and powerA$/hCharge-out rate for the laser, including assist gas and power.

What each input means

Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.

Beam and optics

What this means: Wavelength
Illustration: WavelengthA bar with a dimension line and arrows from one end to the other, marking the length Wavelength.λExample: 10.6 µmWavelength
What it is
The wavelength of the laser light, which sets how small the beam can be focused.
Units and format
Enter a number in µm: micrometres (µm, microns). The form accepts 0.1 µm to 100 µm. Required: the tool does not calculate until every input is valid.
Example
The form opens with 10.6 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
The spot diameter rises in proportion.
Get it right
About 10.6 µm for CO₂ lasers and about 1.06 µm for Nd:YAG and fibre lasers.
What this means: Beam quality factor M²
Illustration: Beam quality factor M²Two bars: a base value and the same value multiplied by Beam quality factor M², the factor.base valuewith factorM²Example: 1.5Beam quality factor M²
What it is
The beam quality factor: how many times larger the focused spot is than a perfect beam of the same wavelength would make.
Units and format
Enter a plain number with no unit. The form accepts 1 to 100. Required: the tool does not calculate until every input is valid.
Example
The form opens with 1.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
The spot diameter rises in proportion.
Get it right
Take it from the laser maker; the handbook quotes about 1.5 for a 1 kW CO₂ laser.
What this means: Raw beam diameter at the lens
Illustration: Raw beam diameter at the lensA circle with a line straight through its centre from edge to edge, marking the diameter Raw beam diameter at the lens.Dmeasured acrossthe centreExample: 20 mmRaw beam diameter at the lens
What it is
The diameter of the unfocused beam where it enters the focusing lens.
Units and format
Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
Example
The form opens with 20 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
A wider beam focuses to a smaller spot.
Get it right
Take it from the beam delivery data; it changes with any beam expander.
What this means: Lens focal length
Illustration: Lens focal lengthA bar with a dimension line and arrows from one end to the other, marking the length Lens focal length.fExample: 127 mmLens focal length
What it is
The focal length of the lens or mirror that focuses the beam onto the work.
Units and format
Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
Example
The form opens with 127 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
The spot rises in proportion and the depth of focus with its square.
Get it right
Read it from the cutting head; shorter lenses suit thin sheet, longer lenses thick sheet.
What this means: Laser power at the work
Illustration: Laser power at the workA motor driving a shaft; Laser power at the work is the rate at which it does work, energy per second.PExample: 2000 WLaser power at the work
What it is
The laser power that reaches the work after losses in the beam path and optics.
Units and format
Enter a number in W: watts. The form accepts 0.000001 W to 1000000 W. Required: the tool does not calculate until every input is valid.
Example
The form opens with 2000 W as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Power density and cutting speed rise in proportion.
Get it right
Use the power setting for the cut, less any known delivery losses.
What this means: Least power density the cut needs
Illustration: Least power density the cut needsItems moving past a point on a conveyor; Least power density the cut needs is how many pass in each unit of time.count pointHreqExample: 1000000 W/cm²Least power density the cut needs
What it is
The power density at the work that your material and process need to cut reliably.
Units and format
Enter a number in W/cm²: W/cm². The form accepts 0.000001 W/cm² or more. Required: the tool does not calculate until every input is valid.
Example
The form opens with 1000000 W/cm² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Only moves the power density pass line.
Get it right
Take it from the laser maker or your own trials; cutting metals usually needs around a million W/cm² or more.
What this means: Spot growth allowed across the depth of focus
Illustration: Spot growth allowed across the depth of focusA bar of 100 parts with the share marked; Spot growth allowed across the depth of focus is that share out of 100. The bar follows the value you type.0 %100 %gExample: 5%Spot growth allowed across the depth of focus
What it is
How much the spot may grow either side of focus and still count as in focus.
Units and format
Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0.1% to 100%. Required: the tool does not calculate until every input is valid.
Example
The form opens with 5% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
A larger allowance gives a longer depth of focus.
Get it right
The handbook defines depth of focus as the range over which the spot changes by 5 %.

Sheet and cut

What this means: Sheet thickness
Illustration: Sheet thicknessThe cross-section of a plate or wall with a dimension across its thickness, marking Sheet thickness.tsection through the materialExample: 3 mmSheet thickness
What it is
The thickness of the sheet being cut.
Units and format
Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
Example
The form opens with 3 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
The estimated cutting speed falls in proportion.
Get it right
Use the nominal thickness of the sheet.
What this means: Surface height variation the head does not foll…
Illustration: Surface height variation the head does not followA nominal size line with an upper and a lower limit around it; parts inside the band are acceptable. The figure illustrates Surface height variation the head does not follow.upperlowerΔzExample: 0.3 mmSurface height variation the head does not fo…
What it is
The height variation of the sheet surface that the cutting head does not follow, which moves the work out of focus.
Units and format
Enter a number in mm: millimetres. The form accepts 0 mm to 100 mm. Required: the tool does not calculate until every input is valid.
Example
The form opens with 0.3 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Only moves the depth of focus pass line.
Get it right
Use zero for a head that follows the surface exactly; measure the sheet's waviness for a fixed head.
What this means: Reference cutting speed from the cutting chart
Illustration: Reference cutting speed from the cutting chartA marker moving along a track; Reference cutting speed from the cutting chart is the distance it covers per unit of time.vrefdistance ÷ timeExample: 3 m/minReference cutting speed from the cutting chart
What it is
A cutting speed from the laser maker's chart for this material and assist gas, at a known power and thickness.
Units and format
Enter a number in m/min: metres per minute. The form accepts 0.000001 m/min to 1000 m/min. Required: the tool does not calculate until every input is valid.
Example
The form opens with 3 m/min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
The estimated speed rises in proportion.
Get it right
Pick a chart point close to your thickness and power so the scaling stays small.
What this means: Power at the reference speed
Illustration: Power at the reference speedA motor driving a shaft; Power at the reference speed is the rate at which it does work, energy per second.PrefExample: 2000 WPower at the reference speed
What it is
The laser power at which the reference cutting speed applies.
Units and format
Enter a number in W: watts. The form accepts 0.000001 W to 1000000 W. Required: the tool does not calculate until every input is valid.
Example
The form opens with 2000 W as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
A higher reference power lowers the estimated speed at your power.
Get it right
Read it from the same chart as the reference speed.
What this means: Thickness at the reference speed
Illustration: Thickness at the reference speedThe cross-section of a plate or wall with a dimension across its thickness, marking Thickness at the reference speed.trefsection through the materialExample: 3 mmThickness at the reference speed
What it is
The sheet thickness at which the reference cutting speed applies.
Units and format
Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
Example
The form opens with 3 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
The estimated speed rises in proportion.
Get it right
Read it from the same chart as the reference speed.
What this means: Cut length per part
Illustration: Cut length per partA bar with a dimension line and arrows from one end to the other, marking the length Cut length per part.LExample: 1500 mmCut length per part
What it is
The total length of cut on one part, including inside cut-outs and holes.
Units and format
Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000000 mm. Required: the tool does not calculate until every input is valid.
Example
The form opens with 1500 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Cutting time and cost rise in proportion.
Get it right
Take it from the nesting or CAM software.
What this means: Pierces per part
Illustration: Pierces per partA row of identical items being counted; Pierces per part is how many there are.nExample: 6Pierces per part
What it is
The number of times the beam pierces the sheet to start a cut on one part.
Units and format
Enter a plain number with no unit. The form accepts 0 to 100000. Use a whole number. Required: the tool does not calculate until every input is valid.
Example
The form opens with 6 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Each pierce adds its pierce time.
Get it right
Count one for the outside profile and one for each inside cut-out.
What this means: Time per pierce
Illustration: Time per pierceA timeline from a start mark to an end mark; Time per pierce is the time between them.startendtpExample: 0.5 sTime per pierce
What it is
The time the laser takes to pierce the sheet once before cutting starts.
Units and format
Enter a number in s: seconds. The form accepts 0 s to 1000 s. Required: the tool does not calculate until every input is valid.
Example
The form opens with 0.5 s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Adds directly to the time per part.
Get it right
Use the pierce time from the machine's cutting table; it rises steeply with thickness.
What this means: Machine rate including gas and power
Illustration: Machine rate including gas and powerA stack of coins and a note representing the money amount Machine rate including gas and power.$Example: 150 A$/hMachine rate including gas and power
What it is
The hourly charge-out rate for the laser, including assist gas, power and the operator.
Units and format
Enter a number in A$/h: A$/h. The form accepts 0 A$/h to 100000 A$/h. Required: the tool does not calculate until every input is valid.
Example
The form opens with 150 A$/h as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
The cost per part rises in proportion.
Get it right
Use your shop's costing rate; oxygen and nitrogen assist differ in cost.

Method and formulas

  1. Focused spot d = 4 M² λ f ÷ (π D) for a beam of wavelength λ and diameter D through a lens of focal length f.
  2. Power density H = 4P ÷ (π d²).
  3. Rayleigh range z_R = π d² ÷ (4 M² λ); the spot grows by a factor √(1 + (z ÷ z_R)²), so the depth of focus for a growth tolerance g is 2 z_R √((1 + g)² − 1).
  4. Cut depth is proportional to power and inversely proportional to speed, so v = v_ref × (P ÷ P_ref) × (t_ref ÷ t).
  5. Time per part = cut length ÷ speed + pierces × pierce time; cost = time × machine rate.
  6. Example: a 0.12855 mm spot gives 15,409,000 W/cm² with 0.52269 mm depth of focus; cutting at 3 m/min takes 33 s a part, A$1.375.

Limitations

  • Gaussian-beam estimates; real spots depend on the optics, their cleanliness and the beam mode.
  • The speed rule holds only within the maker's range for the material, gas and laser; it does not predict cut quality or the thickest sheet that can be cut.
  • Example values are illustrations. Replace them with values for your actual task.

Typical uses

  • Check whether a lens and laser give enough power density for a cut
  • Check the depth of focus against sheet flatness
  • Estimate laser cutting time and cost for a quote

Who it is for

  • Laser cutting operators
  • Manufacturing engineers
  • Estimators

What you get

  • Focused spot diameter and f-number
  • Power density at the work
  • Depth of focus against the surface variation
  • Estimated cutting speed
  • Cut and pierce time and cost per part

Interpreting the result

  • Halving the spot diameter quadruples the power density but shortens the depth of focus four times, so a shorter lens suits thin sheet and a longer one thick or uneven sheet.
  • A shorter wavelength gives a proportionally smaller spot through the same lens.

References

  • Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1487–1494. Topic reference; no source tables or recommended settings are reproduced.

Learn the Concepts Behind This Tool

These KEVOS® Library readings explain the method this tool uses, with worked examples.

KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.

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