foot-lamberts (fL) to apostilbs (asb) conversion

1 fL = 10.76391 asbasb → fL
Formula
1 fL = 10.76391 asb

Understanding foot-lamberts to apostilbs Conversion

A foot-lambert (fL) is a non-SI unit of luminance used mainly in the film, projection, and display industries in the United States; it describes the brightness of a surface emitting or reflecting light. An apostilb (asb) is an older metric luminance unit equal to 1/π1/\pi candela per square metre. Both are "apparent-brightness" units, so this conversion helps translate US projection specifications into the metric apostilb scale.

Conversion Formula

1 fL=10.7639 asb1\ \text{fL} = 10.7639\ \text{asb}

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

asb=fL×10.76391\text{asb} = \text{fL} \times 10.76391

Step-by-Step Example

Convert 25 foot-lamberts to apostilbs.

asb=25×10.76391=269.098 asb\text{asb} = 25 \times 10.76391 = 269.098\ \text{asb}

How to Convert foot-lamberts to apostilbs

Translate a US luminance figure into the metric apostilb scale with one multiplication.

  1. Note the factor: One foot-lambert equals 10.76391 apostilbs.
  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 10.76391.
  4. Read the result: 25×10.76391=269.09825 \times 10.76391 = 269.098 apostilbs.

foot-lamberts to apostilbs conversion table

foot-lamberts (fL)apostilbs (asb)
00
110.76391
221.52782
332.29173
443.05564
553.81955
664.58346
775.34737
886.11128
996.87519
10107.6391
15161.4587
20215.2782
25269.0978
30322.9173
40430.5564
50538.1955
60645.8346
70753.4737
80861.1128
90968.7519
1001076.391
1501614.587
2002152.782
2502690.978
3003229.173
4004305.564
5005381.955
6006458.346
7007534.737
8008611.128
9009687.519
100010763.91
200021527.82
300032291.73
400043055.64
500053819.55
10000107639.1
25000269097.8
50000538195.5
1000001076391
2500002690978
5000005381955
100000010763910

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 apostilb?

The apostilb is an obsolete unit of luminance once used to describe the brightness of diffusely reflecting or emitting surfaces. It belongs to a family of "1/π" luminance units designed to simplify calculations for perfectly diffuse (Lambertian) surfaces.

Definition

One apostilb is defined as one lumen per square metre emitted from a perfectly diffusing surface, which equals 1/π candela per square metre.

1 asb=0.318310 cd/m21\ \text{asb} = 0.318310\ \text{cd/m}^2

Exactly, 1 asb=1π cd/m2=10−4 lambert1\ \text{asb} = \frac{1}{\pi}\ \text{cd/m}^2 = 10⁻⁴\ \text{lambert}.

Origin and History

The apostilb was part of an early-20th-century set of photometric units (alongside the lambert and foot-lambert) built around the factor 1/π so that a Lambertian surface illuminated to a given number of lux would have a numerically equal luminance. The prefix "apo-" distinguished it from the stilb.

Law and Notable Facts

The apostilb is not an SI unit and is now essentially obsolete, replaced by the candela per square metre. Its defining convenience was that a perfect diffuser receiving an illuminance of one lux has a luminance of exactly one apostilb.

Real-World Examples and Conversions

  • A white matte surface at 1 lux illuminance: about 1 apostilb.
  • 1 asb=1π cd/m2≈0.318310 cd/m21\ \text{asb} = \frac{1}{\pi}\ \text{cd/m}^2 \approx 0.318310\ \text{cd/m}^2.
  • 1 cd/m2=π apostilbs≈3.14159 asb1\ \text{cd/m}^2 = \pi\ \text{apostilbs} \approx 3.14159\ \text{asb}.
  • 104 apostilbs=1 lambert≈3183.10 cd/m210⁴\ \text{apostilbs} = 1\ \text{lambert} \approx 3183.10\ \text{cd/m}^2.

Frequently Asked Questions

How many apostilbs are in one foot-lambert?

One foot-lambert equals about 10.7639 apostilbs, the same numeric ratio that relates square feet to square metres.

What do foot-lamberts and apostilbs measure?

Both measure luminance, the perceived brightness of a surface; foot-lamberts are common in US cinema and display work, while apostilbs are an older metric luminance unit.

How is the apostilb related to candela per square metre?

One apostilb equals 1/π1/\pi cd/m² (about 0.3183 cd/m²), because apostilbs assume a perfectly diffusing surface.

Where is this conversion useful?

It helps engineers translate US projection-screen brightness specifications, often quoted in foot-lamberts, into the metric apostilb scale used in older European lighting references.

How do I convert 14 foot-lamberts to apostilbs?

Multiply 14 by 10.76391 to get about 150.695 apostilbs, close to the SMPTE cinema white-level recommendation.

People also convert

fL to cd/m2fL to ntfL to sbfL to L

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