Convert spectral linewidth between wavelength, frequency, wavenumber and photon energy — then get coherence length, coherence time and Q factor. Exact physics, zero approximations hidden.
01Linewidth converter
Enter the center wavelength λ₀ and the linewidth in any unit — Δλ, Δν, Δν̃ or ΔE. Every other representation is computed with the exact two-point formula. It works as a laser linewidth to frequency converter: wavelength linewidth to frequency linewidth (linewidth wavelength to frequency conversion), nm linewidth to GHz converter, nm linewidth to Hz converter, pm linewidth to MHz, linewidth cm⁻¹ to GHz and back, and linewidth to eV — a complete spectral linewidth conversion toolkit and FWHM linewidth reference. Use it as a mode linewidth calculator and spectral purity laser calculator.
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frequency linewidth Δν
Quantity
Value
Notes
02Schawlow–Townes quantum limit
The fundamental linewidth floor from quantum noise: Δν = π·h·ν·Γ² / P. This Schawlow–Townes (Schawlow Townes) calculator implements the laser linewidth equation (Schawlow Townes linewidth formula) — the quantum noise linewidth limit. Real lasers are broader — technical noise dominates — but nothing beats this limit.
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Schawlow–Townes linewidth ΔνST
This is a lower bound. Measured linewidths are larger because of pump noise, thermal drift, vibrations and electronics — the technical noise floor.
03Typical linewidths of common lasers
Order-of-magnitude reference values — always use your device datasheet for real work. Linewidth in frequency, coherence length and Q factor computed with the exact formulas above. Covers HeNe laser linewidth, He-Ne 632.8 nm linewidth, Nd:YAG / Nd YAG laser linewidth, diode laser linewidth, CO2 laser linewidth, fiber laser linewidth 1550 nm and typical laser pointer linewidth.
Laser
λ₀
Typical Δν
Coherence length
Q factor
HeNe
632.8 nm
1.497 GHz
20.02 cm
316,400
Nd:YAG (single-frequency)
1064 nm
5 kHz
59.96 km
56,350,000,000
Red diode
650 nm
70.96 GHz
4.225 mm
6,500
DPSS green (SLM)
532 nm
5 MHz
59.96 m
112,700,000
Fiber (narrow-linewidth)
1550 nm
1 kHz
299.8 km
193,400,000,000
CO₂
10.6 µm
1 MHz
299.8 m
28,280,000
Illustrative values for comparison only — real devices vary by orders of magnitude between free-running, stabilized and single-frequency designs.
04How the math works
Every number on this page comes from these definitions. No hidden approximations.
Δν = c / (λ₀ − Δλ/2) − c / (λ₀ + Δλ/2) · exact, valid for any width
Δν ≈ c · Δλ / λ₀² · first-order approximation (shown with its error)
Δν̃ = Δν / 2.99792458×10¹⁰ · wavenumber linewidth in cm⁻¹
ΔE = h · Δν · energy linewidth (J, also shown in eV)
ΔνST = π · h · ν · Γ² / P · Schawlow–Townes quantum limit
The coherence length formula — coherence length from linewidth — uses the standard Lc = c/Δν convention (Wikipedia “Coherence length”, RP Photonics encyclopedia); the Lorentzian variant Lc = c/(π·Δν) is also displayed for comparison. The same two-point formula doubles as a laser bandwidth converter: wavelength bandwidth to frequency bandwidth, i.e. a spectral bandwidth converter and optical bandwidth calculator. Constants: c = 299,792,458 m/s (exact), h = 6.62607015×10⁻³⁴ J·s (exact), e = 1.602176634×10⁻¹⁹ J/eV (exact).
Scope check — what this tool is (and isn't)
This tool: spectral linewidth — converting Δλ ↔ Δν ↔ Δν̃ ↔ ΔE, coherence length, coherence time, Q factor and the Schawlow–Townes limit.
Not this tool: laser brightness / radiance (power per area per solid angle), beam divergence, or spot size — that is a different property of the beam. For brightness, use our laser brightness calculator.
05Frequently asked questions
Short, precise answers to the questions people actually search for.
What is the linewidth of a laser?
The linewidth of a laser is the full width at half maximum (FWHM) of the power spectrum of its output. It measures how much the emitted light deviates from perfect monochromaticity: a real laser emits a narrow spread of frequencies around its center frequency, and the linewidth quantifies that spread in wavelength (Δλ), frequency (Δν), wavenumber or energy units. This FWHM linewidth is the standard laser spectral linewidth definition used in datasheets.
How do I convert laser linewidth from nm to GHz?
Use the exact two-point formula Δν = c/(λ₀−Δλ/2) − c/(λ₀+Δλ/2), where λ₀ is the center wavelength and c is the speed of light. For example, a HeNe laser at 632.8 nm with Δλ = 0.002 nm has Δν ≈ 1.50 GHz. The converter above does this calculation instantly in both directions.
What is the difference between laser linewidth and laser bandwidth?
Linewidth describes the frequencies actually occupied by the laser output (the FWHM of the emission spectrum), while bandwidth is the wider range of frequencies the device could in principle emit, which depends on the gain medium and cavity design. Bandwidth is usually taken from the device datasheet; linewidth is what you measure or convert with this tool. In short, the laser linewidth vs bandwidth question is: linewidth is what the laser emits, bandwidth is what it could emit.
How do you calculate coherence length from linewidth?
Temporal coherence length is Lc = c/Δν, where Δν is the frequency linewidth. A HeNe laser with 1.5 GHz linewidth has Lc ≈ 0.20 m, meaning interference fringes stay visible for path differences up to about 20 cm. Narrower linewidth means longer coherence length, which is why single-frequency lasers are used in interferometry. This coherence length vs linewidth trade-off (linewidth vs coherence length) is fundamental: halve the linewidth, double the coherence length.
What is the Q factor of a laser?
The Q factor (quality factor) is Q = ν₀/Δν = λ₀/Δλ, the Q factor from linewidth and center wavelength, and the same definition gives the cavity Q factor. It describes how sharply the laser oscillates: a HeNe laser with 1.5 GHz linewidth at 474 THz has Q ≈ 316,000, while a 1 kHz-linewidth fiber laser reaches Q above 10¹¹.
What is the Schawlow–Townes linewidth?
The Schawlow–Townes linewidth is the fundamental quantum limit of laser linewidth, Δν = π·h·ν·Γ²/P, where h is the Planck constant, ν the laser frequency, Γ the cold-cavity linewidth and P the mode power. For a 1 W HeNe laser with 1 GHz cavity linewidth it gives about 0.99 Hz. Real lasers are broader because of technical noise.
What is a narrow linewidth laser?
A narrow linewidth laser emits light with a very high degree of monochromaticity (laser monochromaticity) — typically kilohertz linewidth or below. This requires single-frequency operation, suppression of mode hopping, and minimization of phase noise. Narrow linewidth lasers are used in coherent sensing, spectroscopy, interferometry and optical communications.
What is the typical linewidth of a HeNe laser?
A typical HeNe laser at 632.8 nm has a linewidth of about 0.002 nm, which converts to roughly 1.5 GHz in frequency. Its coherence length is therefore about 0.20 m and its Q factor about 316,000. Stabilized single-frequency HeNe lasers can be far narrower.
How do I convert linewidth to wavenumbers (cm⁻¹)?
Divide the frequency linewidth by the speed of light expressed in cm/s: Δν̃ = Δν / 2.99792458×10¹⁰ cm⁻¹. For example, 1.5 GHz corresponds to about 0.05 cm⁻¹. The converter above shows the wavenumber linewidth automatically alongside every other unit, doubling as a GHz to cm⁻¹ converter.
How do I convert linewidth to photon energy in eV?
Multiply the frequency linewidth by the Planck constant and divide by the elementary charge: ΔE = h·Δν / e. A 1.5 GHz linewidth corresponds to about 6.2 µeV. The tool is a linewidth to eV converter and photon energy linewidth calculator, displaying the energy linewidth in both joules and electronvolts.
Does this calculator use the exact formula or the approximation?
It uses the exact two-point formula Δν = c/(λ₀−Δλ/2) − c/(λ₀+Δλ/2), which stays correct even for wide bandwidths. It also shows the common first-order approximation Δν ≈ c·Δλ/λ₀² and its relative error, so you can see when the approximation is safe to use.
Why is coherence length sometimes written as c/(π·Δν)?
For a Lorentzian spectral line of FWHM Δν, the Wiener–Khinchin theorem gives a coherence time of 1/(π·Δν), hence Lc = c/(π·Δν). The widely used general convention is Lc = c/Δν. This tool uses Lc = c/Δν as the primary result and also displays the Lorentzian variant so you can compare.
What is the difference between laser linewidth and laser brightness?
Linewidth describes the spectral width of the emission — how monochromatic the light is. Brightness (radiance) describes how much optical power is concentrated per unit area and solid angle — how intense and directional the beam is. They are different properties; use our laser brightness calculator at nrtechstudio.com/tools/laser-brightness/ for brightness and radiance.
Is my data sent anywhere when I use this tool?
No. This laser linewidth converter runs entirely in your browser with no network requests. Your inputs never leave your device, which also means it works offline once the page is loaded.
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