Lambert (unit)

The lambert (symbol L^[1][2]) is a non-SI metric unit of luminance named for Johann Heinrich Lambert (1728–1777), a Swiss mathematician, physicist and astronomer. A related unit of luminance, the foot-lambert, is used in the lighting, cinema and flight simulation industries. The SI unit is the candela per square metre (cd/m²).

Definition

1 lambert (L) = ${\displaystyle {\frac {1}{\pi }}}$ candela per square centimetre (0.3183 cd/cm²) or ${\displaystyle {\frac {10^{4}}{\pi }}}$ cd m⁻²

Units of luminance

v t e		cd/m2 (SI unit) ≡ nit ≡ lm/m2/sr	stilb (sb) (CGS unit) ≡ cd/cm2		apostilb (asb) ≡ blondel	bril	skot (sk)	lambert (L)		foot-lambert (fL) = 1 ⁄ π cd/ft2
1 cd/m2	=	1	10−4		π ≈ 3.142	107 π ≈ 3.142×107	103 π ≈ 3.142×103	10−4 π ≈ 3.142×10−4		0.30482 π ≈ 0.2919
1 sb	=	104	1		104 π ≈ 3.142×104	1011 π ≈ 3.142×1011	107 π ≈ 3.142×107	π ≈ 3.142		30.482 π ≈ 2919
1 asb	=	1 ⁄ π ≈ 0.3183	10−4 ⁄ π ≈ 3.183×10−5		1	107	103	10−4		0.30482 ≈ 0.09290
1 bril	=	10−7 ⁄ π ≈ 3.183×10−8	10−11 ⁄ π ≈ 3.183×10−12		10−7	1	10−4	10−11		0.30482×10−7 ≈ 9.290×10−9
1 sk	=	10−3 ⁄ π ≈ 3.183×10−4	10−7 ⁄ π ≈ 3.183×10−8		10−3	104	1	10−7		0.30482×10−3 ≈ 9.290×10−5
1 L	=	104 ⁄ π ≈ 3183	1 ⁄ π ≈ 0.3183		104	1011	107	1		0.30482×104 ≈ 929.0
1 fL	=	1 ⁄ 0.30482 ⁄ π ≈ 3.426	1 ⁄ 30.482 ⁄ π ≈ 3.426×10−4		1 ⁄ 0.30482 ≈ 10.76	107 ⁄ 0.30482 ≈ 1.076×108	103 ⁄ 0.30482 ≈ 1.076×104	10−4 ⁄ 0.30482 ≈ 1.076×10−3		1

See also

Other units of luminance:

• Apostilb (asb)
• Blondel (blondel)
• Bril (bril)
• Nit (nit)
• Stilb (sb)
• Skot (sk)

SI photometry quantities

• v
• t
• e

Quantity		Unit		Dimension [nb 1]	Notes
Name	Symbol[nb 2]	Name	Symbol
Luminous energy	Qv[nb 3]	lumen second	lm⋅s	T⋅J	The lumen second is sometimes called the talbot.
Luminous flux, luminous power	Φv[nb 3]	lumen (= candela steradian)	lm (= cd⋅sr)	J	Luminous energy per unit time
Luminous intensity	Iv	candela (= lumen per steradian)	cd (= lm/sr)	J	Luminous flux per unit solid angle
Luminance	Lv	candela per square metre	cd/m2 (= lm/(sr⋅m2))	L−2⋅J	Luminous flux per unit solid angle per unit projected source area. The candela per square metre is sometimes called the nit.
Illuminance	Ev	lux (= lumen per square metre)	lx (= lm/m2)	L−2⋅J	Luminous flux incident on a surface
Luminous exitance, luminous emittance	Mv	lumen per square metre	lm/m2	L−2⋅J	Luminous flux emitted from a surface
Luminous exposure	Hv	lux second	lx⋅s	L−2⋅T⋅J	Time-integrated illuminance
Luminous energy density	ωv	lumen second per cubic metre	lm⋅s/m3	L−3⋅T⋅J
Luminous efficacy (of radiation)	K	lumen per watt	lm/W	M−1⋅L−2⋅T3⋅J	Ratio of luminous flux to radiant flux
Luminous efficacy (of a source)	η[nb 3]	lumen per watt	lm/W	M−1⋅L−2⋅T3⋅J	Ratio of luminous flux to power consumption
Luminous efficiency, luminous coefficient	V			1	Luminous efficacy normalized by the maximum possible efficacy
See also: SI Photometry Radiometry

1. The symbols in this column denote dimensions; "L", "T" and "J" are for length, time and luminous intensity respectively, not the symbols for the units litre, tesla and joule.
2. Standards organizations recommend that photometric quantities be denoted with a subscript "v" (for "visual") to avoid confusion with radiometric or photon quantities. For example: USA Standard Letter Symbols for Illuminating Engineering USAS Z7.1-1967, Y10.18-1967
3. Alternative symbols sometimes seen: W for luminous energy, P or F for luminous flux, and ρ for luminous efficacy of a source.