lamberts (L) to foot-lamberts (fL) conversion

1 L = 929.0304 fLfL → L
Formula
1 L = 929.0304 fL

Understanding Lamberts to Foot-Lamberts Conversion

The lambert (L) is a CGS luminance unit for a Lambertian surface emitting 1 lumen per square centimetre. The foot-lambert (fL) is its imperial cousin, defined as the luminance of a perfect diffuser emitting or reflecting 1 lumen per square foot, and it remains common in cinema projection and display standards in the United States. Converting lamberts to foot-lamberts is useful when reconciling metric photometry with projection-brightness specifications quoted in fL.

Conversion Formula

1 L=929.030 fL1\ \text{L} = 929.030\ \text{fL}

To convert Lamberts to Foot-Lamberts, multiply by this factor:

fL=L×929.0304\text{fL} = \text{L} \times 929.0304

Step-by-Step Example

Convert 25 Lamberts to Foot-Lamberts.

fL=25×929.0304=23225.8 fL\text{fL} = 25 \times 929.0304 = 23225.8\ \text{fL}

How to Convert Lamberts to Foot-Lamberts

Convert the metric lambert to the imperial foot-lambert used in projection with one step.

  1. Note the lambert value: record the luminance in L.
  2. Multiply by 929.0304: this converts from a per-cm² to a per-ft² basis.
  3. Calculate: for 25 L, compute 25×929.030425 \times 929.0304.
  4. Report the result: the luminance is 23,225.8 fL.

lamberts to foot-lamberts conversion table

lamberts (L)foot-lamberts (fL)
00
1929.0304
21858.061
32787.091
43716.122
54645.152
65574.182
76503.213
87432.243
98361.274
109290.304
1513935.46
2018580.61
2523225.76
3027870.91
4037161.22
5046451.52
6055741.82
7065032.13
8074322.43
9083612.74
10092903.04
150139354.6
200185806.1
250232257.6
300278709.1
400371612.2
500464515.2
600557418.2
700650321.3
800743224.3
900836127.4
1000929030.4
20001858061
30002787091
40003716122
50004645152
100009290304
2500023225760
5000046451520
10000092903040
250000232257600
500000464515200
1000000929030400

What is the Lambert?

The lambert is a non-SI unit of luminance, describing how much light is emitted or reflected from a surface toward an observer. It is named after the Swiss-German polymath Johann Heinrich Lambert and appears mainly in older optics, photometry, and lighting literature.

Definition

The lambert is defined so that a perfectly diffusing (Lambertian) surface emitting or reflecting a total luminous flux of one lumen per square centimetre has a luminance of one lambert.

1 L=3183.10 cd/m21\ \text{L} = 3183.10\ \text{cd/m}^2

Equivalently, 1 L=1π cd/cm2=104π cd/m21\ \text{L} = \frac{1}{\pi}\ \text{cd/cm}^2 = \frac{10⁴{\pi}\ \text{cd/m}^2. The factor of π\pi enters because luminance in candela per unit area relates to the emitted lumens per unit area through the geometry of a Lambertian (cosine-law) emitter. Sub-multiples such as the millilambert (mL) and microlambert are common in practice.

Origin and History

The unit honors Johann Heinrich Lambert (1728–1777), whose 1760 work Photometria laid the mathematical foundations of photometry, including the cosine emission law of diffuse surfaces. The lambert itself was proposed in the early 20th century as photometry was being systematized, and it saw wide use before the SI candela-per-square-metre (nit) became standard.

Law and Notable Facts

The lambert is not part of the SI and is discouraged in modern metrology, but it survives in legacy instruments and texts. A key convenience of the lambert family is that a perfect diffuse reflector illuminated by one lux has a luminance of exactly 1π×10−4\tfrac{1}{\pi}\times10^{-4} lambert, tidily linking illuminance and luminance for ideal surfaces.

Real-World Examples and Conversions

  • A surface of 1 lambert equals about 3183 cd/m², roughly the brightness of a bright fluorescent lamp diffuser.
  • 1 millilambert = 3.18310 cd/m², close to comfortable indoor lighting levels.
  • The closely related foot-lambert (used for cinema screens) equals about 3.426 cd/m²; standard theater screen luminance of 14 fL corresponds to roughly 48 cd/m².
  • 1 lambert ≈ 929.03 foot-lamberts.

What is the Foot-Lambert?

The foot-lambert is a non-SI unit of luminance, expressing the brightness of a surface as seen by an observer. It remains widely used in the cinema, projection, and display industries in the United States, where screen brightness is often specified in foot-lamberts.

Definition

The foot-lambert is defined so that a perfectly diffusing (Lambertian) surface emitting or reflecting a total luminous flux of one lumen per square foot has a luminance of one foot-lambert.

1 fL=3.42626 cd/m21\ \text{fL} = 3.42626\ \text{cd/m}^2

Equivalently, 1 fL=1π cd/ft21\ \text{fL} = \frac{1}{\pi}\ \text{cd/ft}^2. As with the lambert, the factor of π\pi arises from the cosine emission geometry of a Lambertian source. Because one square foot equals 0.09290304 m20.09290304\ \text{m}^2, the conversion follows directly: 1π×0.09290304 cd/m2=3.42626 cd/m2\frac{1}{\pi \times 0.09290304}\ \text{cd/m}^2 = 3.42626\ \text{cd/m}^2.

Origin and History

The foot-lambert is the imperial-unit counterpart of the lambert, both descending from Johann Heinrich Lambert's foundational photometry. It became entrenched in mid-20th-century American engineering practice, particularly in cinema, where SMPTE standards long specified projected picture brightness in foot-lamberts.

Law and Notable Facts

The foot-lambert is not an SI unit, but it persists in professional standards. SMPTE recommends an open-gate (unmodulated) screen luminance of 14 fL (≈ 48 cd/m²) for film projection and 16 fL peak white for digital cinema in a dark theater. HDR home displays, by contrast, target hundreds to over a thousand cd/m².

Real-World Examples and Conversions

  • 14 foot-lamberts (SMPTE film reference) ≈ 47.97 cd/m².
  • 1 foot-lambert ≈ 3.42626 cd/m² ≈ 0.001076 lambert.
  • A typical office display of 250 cd/m² is about 73 foot-lamberts.
  • 1 lambert ≈ 929.03 foot-lamberts.

Frequently Asked Questions

How many foot-lamberts are in one lambert?

One lambert equals 929.0304 foot-lamberts, reflecting the ratio between the square-centimetre and square-foot area bases.

How do I convert lamberts to foot-lamberts?

Multiply the lambert value by 929.0304. For example, 5 L equals about 4645.15 fL.

Where are foot-lamberts still used?

They are widely used in North American cinema and projection standards, where target screen luminance is often specified around 14 fL for film.

Why is the factor about 929?

It arises because one square foot equals 929.0304 square centimetres, so the lumen-per-area definitions differ by that same amount.

How do I reverse the conversion?

Multiply the foot-lambert value by 0.001076391 to return to lamberts.

People also convert

L to cd/m2L to ntL to sbL to asb

Complete lamberts conversion table

L
UnitResult
candelas per square metre (cd/m2)3183.099 cd/m2
nits (nt)3183.099 nt
stilbs (sb)0.3183099 sb
apostilbs (asb)10000 asb
foot-lamberts (fL)929.0304 fL

Luminance conversions