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Radiometry ↔ Photometry Converter (W ↔ lm)

Convert radiant power in watts to luminous flux in lumens (and back) for light of a chosen wavelength, using the CIE photopic V(λ) curve.

nm

Green 555 nm, red laser 650 nm, blue 450 nm.

Luminous flux

683 lm

Luminous efficacy at this wavelength
683 lm/W
V(λ)
1
Radiant power
1 W

Monochromatic light at 555 nm (standard air): V(λ) = 1, so 1 W = 683 lm. Values from the CIE 018:2019 photopic table (daylight vision).

Show the work

  1. Eye sensitivity V(λ) at 555 nm

    CIE 018:2019 photopic table

    1

  2. Luminous efficacy at this wavelength

    K = 683 lm/W × V(λ)

    683 × 1 = 683 lm/W

  3. Luminous flux: efficacy × radiant power

    Φv = K × Φe

    683 × 1 = 683 lm

How it works

Φv (lm) = 683 lm/W × V(λ) × Φe (W), with V(λ) the CIE photopic luminous efficiency at the wavelength (1 nm table, linear in between).

For light of one wavelength (a laser or narrow LED). White or broad-spectrum light needs its whole spectrum, so a bulb's lumens per watt can't be found this way. V(λ): CIE 018:2019 Table 1, wavelengths in standard air, 360–830 nm (CIE dataset doi:10.25039/CIE.DS.dktna2s3, CC BY-SA 4.0). Km = 683 lm/W from the SI definition of the candela.

Questions

How does the radiometry ↔ photometry converter work?
Φv (lm) = 683 lm/W × V(λ) × Φe (W), with V(λ) the CIE photopic luminous efficiency at the wavelength (1 nm table, linear in between).
What does it assume?
For light of one wavelength (a laser or narrow LED). White or broad-spectrum light needs its whole spectrum, so a bulb's lumens per watt can't be found this way. V(λ): CIE 018:2019 Table 1, wavelengths in standard air, 360–830 nm (CIE dataset doi:10.25039/CIE.DS.dktna2s3, CC BY-SA 4.0). Km = 683 lm/W from the SI definition of the candela.
Why is 555 nm special?
The eye is most sensitive there in daylight (V = 1), so 1 W of 555 nm light is 683 lm — the most any light can give per watt.
Does this tell me how many lumens my bulb makes?
No — a bulb's watts are electrical input and its light covers many wavelengths. This tool is for a known amount of optical power at one wavelength.

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