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Beam Divergence Formula

GoBeam Divergence given Diameter of Spot Formula

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Beam Divergence is the angle made by the beam incident on surface of metal. Check FAQs

α = \sqrt{\frac{4 \cdot P}{π \cdot {f lens}^{2} \cdot δ p \cdot ΔT}}

α - Beam Divergence?P - Laser Energy Output?f_lens - Focal Length of Lens?δ_p - Power Density of Laser Beam?ΔT - Laser Beam Duration?π - Archimedes' constant?

Beam Divergence Example

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With units

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Here is how the Beam Divergence equation looks like with Values.

Here is how the Beam Divergence equation looks like with Units.

Here is how the Beam Divergence equation looks like.

0.0012 = \sqrt{\frac{4 \cdot 10.39}{3.1416 \cdot 3^{2} \cdot 9.49 \cdot 10.2}}

0.0012rad = \sqrt{\frac{4 \cdot 10.39W}{3.1416 \cdot {3m}^{2} \cdot 9.49W/cm² \cdot 10.2s}}

0.0012 = \sqrt{\frac{4 \cdot 10.39}{3.1416 \cdot 3^{2} \cdot 9.49 \cdot 10.2}}

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Beam Divergence Solution

Follow our step by step solution on how to calculate Beam Divergence?

FIRST Step Consider the formula

α = \sqrt{\frac{4 \cdot P}{π \cdot {f lens}^{2} \cdot δ p \cdot ΔT}}

Next Step Substitute values of Variables

∴

α = \sqrt{\frac{4 \cdot 10.39W}{π \cdot {3m}^{2} \cdot 9.49W/cm² \cdot 10.2s}}

Next Step Substitute values of Constants

∴

α = \sqrt{\frac{4 \cdot 10.39W}{3.1416 \cdot {3m}^{2} \cdot 9.49W/cm² \cdot 10.2s}}

Next Step Convert Units

∴

α = \sqrt{\frac{4 \cdot 10.39W}{3.1416 \cdot {3m}^{2} \cdot 94900W/m² \cdot 10.2s}}

Next Step Prepare to Evaluate

∴

α = \sqrt{\frac{4 \cdot 10.39}{3.1416 \cdot 3^{2} \cdot 94900 \cdot 10.2}}

Next Step Evaluate

∴

α = 0.00123227712391686rad

LAST Step Rounding Answer

∴

α = 0.0012rad

Beam Divergence Formula Elements

Variables

Constants

Functions

Beam Divergence

Beam Divergence is the angle made by the beam incident on surface of metal.

Symbol: α

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Beam Divergence

Laser Energy Output

Laser Energy Output refers to the amount of energy emitted by a laser over a specific period of time.

Symbol: P

Measurement: PowerUnit: W

Note: Value should be greater than 0.

Formulas to find Laser Energy Output

Focal Length of Lens

Focal Length of Lens is determined when lens is focused at infinity. Lens focal length tells us angle of view and how much of scene will be captured. The longer focal length, a narrower angle of view.

Symbol: f_lens

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Focal Length of Lens

Power Density of Laser Beam

Power Density of Laser Beam is the power per unit area of beam.

Symbol: δ_p

Measurement: Heat Flux DensityUnit: W/cm²

Note: Value should be greater than 0.

Formulas to find Power Density of Laser Beam

Laser Beam Duration

Laser Beam Duration is the time for which laser beam is incident on the work surface.

Symbol: ΔT

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Laser Beam Duration

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Beam Divergence

Go Beam Divergence given Diameter of Spot

α = \frac{d spot}{f lens}

Other formulas in Power Density of Laser Beam category

Go Power Density of Laser Beam

δ p = \frac{4 \cdot P}{π \cdot {f lens}^{2} \cdot α^{2} \cdot ΔT}

Go Laser Energy Output

P = \frac{δ p \cdot π \cdot {f lens}^{2} \cdot α^{2} \cdot ΔT}{4}

Go Focal Length of Lens

f lens = \sqrt{\frac{4 \cdot P}{π \cdot δ p \cdot α^{2} \cdot ΔT}}

Go Pulse Duration of Laser

ΔT = \frac{4 \cdot P}{π \cdot {f lens}^{2} \cdot α^{2} \cdot δ p}

How to Evaluate Beam Divergence?

Beam Divergence evaluator uses Beam Divergence = sqrt((4*Laser Energy Output)/(pi*Focal Length of Lens^2*Power Density of Laser Beam*Laser Beam Duration)) to evaluate the Beam Divergence, The Beam Divergence formula is defined as the angle of divergence of the laser beam used in Laser beam machining. Beam Divergence is denoted by α symbol.

How to evaluate Beam Divergence using this online evaluator? To use this online evaluator for Beam Divergence, enter Laser Energy Output (P), Focal Length of Lens (f_lens), Power Density of Laser Beam (δ_p) & Laser Beam Duration (ΔT) and hit the calculate button.

FAQs on Beam Divergence

What is the formula to find Beam Divergence?

The formula of Beam Divergence is expressed as Beam Divergence = sqrt((4*Laser Energy Output)/(pi*Focal Length of Lens^2*Power Density of Laser Beam*Laser Beam Duration)). Here is an example- 0.001232 = sqrt((4*10.39)/(pi*3^2*94900*10.2)).

How to calculate Beam Divergence?

With Laser Energy Output (P), Focal Length of Lens (f_lens), Power Density of Laser Beam (δ_p) & Laser Beam Duration (ΔT) we can find Beam Divergence using the formula - Beam Divergence = sqrt((4*Laser Energy Output)/(pi*Focal Length of Lens^2*Power Density of Laser Beam*Laser Beam Duration)). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Beam Divergence?

Here are the different ways to Calculate Beam Divergence-

Beam Divergence=Spot Diameter/Focal Length of Lens

Can the Beam Divergence be negative?

No, the Beam Divergence, measured in Angle cannot be negative.

Which unit is used to measure Beam Divergence?

Beam Divergence is usually measured using the Radian[rad] for Angle. Degree[rad], Minute[rad], Second[rad] are the few other units in which Beam Divergence can be measured.

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Beam Divergence Formula

​GoBeam Divergence given Diameter of Spot Formula

Beam Divergence Example

Beam Divergence Solution

Beam Divergence Formula Elements

Other Formulas to find Beam Divergence

Other formulas in Power Density of Laser Beam category

How to Evaluate Beam Divergence?

FAQs on Beam Divergence

Variable Name

GoBeam Divergence given Diameter of Spot Formula