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

1 fL = 0.001076391 LL → fL
Formula
1 fL = 0.001076391 L

Understanding foot-lamberts to lamberts Conversion

A foot-lambert (fL) is a US customary luminance unit representing the brightness of a surface in the foot-pound-second system. A lambert (L) is the corresponding centimetre-gram-second (CGS) luminance unit, equal to 1/π1/\pi candela per square centimetre. Both are named after Johann Lambert and describe apparent brightness; converting foot-lamberts to lamberts moves between the imperial and CGS versions of the same idea.

Conversion Formula

1 fL=0.00107639 L1\ \text{fL} = 0.00107639\ \text{L}

To convert foot-lamberts to lamberts, multiply by this factor:

L=fL×0.001076391\text{L} = \text{fL} \times 0.001076391

Step-by-Step Example

Convert 25 foot-lamberts to lamberts.

L=25×0.001076391=0.0269098 L\text{L} = 25 \times 0.001076391 = 0.0269098\ \text{L}

How to Convert foot-lamberts to lamberts

Move between the imperial and CGS luminance units with one multiplication.

  1. Note the factor: One foot-lambert equals 0.001076391 lamberts.
  2. Take your luminance in foot-lamberts: Start with the value to convert, for example 25 fL.
  3. Multiply: Multiply the foot-lambert value by 0.001076391.
  4. Read the result: 25×0.001076391=0.026909825 \times 0.001076391 = 0.0269098 lamberts.

foot-lamberts to lamberts conversion table

foot-lamberts (fL)lamberts (L)
00
10.001076391
20.002152782
30.003229173
40.004305564
50.005381955
60.006458346
70.007534737
80.008611128
90.009687519
100.01076391
150.01614587
200.02152782
250.02690978
300.03229173
400.04305564
500.05381955
600.06458346
700.07534737
800.08611128
900.09687519
1000.1076391
1500.1614587
2000.2152782
2500.2690978
3000.3229173
4000.4305564
5000.5381955
6000.6458346
7000.7534737
8000.8611128
9000.9687519
10001.076391
20002.152782
30003.229173
40004.305564
50005.381955
1000010.76391
2500026.90978
5000053.81955
100000107.6391
250000269.0978
500000538.1955
10000001076.391

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.

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.

Frequently Asked Questions

How many lamberts are in one foot-lambert?

One foot-lambert equals about 0.00107639 lamberts, since the lambert is a much larger CGS-based unit.

How many foot-lamberts make one lambert?

About 929.03 foot-lamberts equal one lambert, the same factor that relates square feet to square centimetres.

What is the difference between a lambert and a foot-lambert?

The lambert uses the centimetre as its length base while the foot-lambert uses the foot, so a lambert represents a far brighter surface for the same numeric value.

Who were these units named after?

Both are named after Johann Heinrich Lambert, the 18th-century mathematician who pioneered photometry and the study of light reflection.

How do I convert 100 foot-lamberts to lamberts?

Multiply 100 by 0.001076391 to get about 0.107639 lamberts.

People also convert

fL to cd/m2fL to ntfL to sbfL to asb

Complete foot-lamberts conversion table

fL
UnitResult
candelas per square metre (cd/m2)3.426259 cd/m2
nits (nt)3.426259 nt
stilbs (sb)0.0003426259 sb
apostilbs (asb)10.76391 asb
lamberts (L)0.001076391 L

Luminance conversions