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

1 asb = 0.09290304 fLfL → asb
Formula
1 asb = 0.09290304 fL

Understanding apostilbs to foot-lamberts Conversion

The apostilb (asb) is a metric luminance unit equal to 1/π cd/m², based on a perfectly diffusing surface illuminated to one lux. The foot-lambert (fL) is the corresponding US customary unit, the luminance of a perfect diffuser emitting one lumen per square foot, equal to 1/π candela per square foot. Both are "apparent" luminance units, so converting between them is essentially a metric-to-imperial area conversion widely seen in projection, cinema, and display engineering.

Conversion Formula

1 asb=0.0929030 fL1\ \text{asb} = 0.0929030\ \text{fL}

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

fL=asb×0.09290304\text{fL} = \text{asb} \times 0.09290304

Step-by-Step Example

Convert 25 apostilbs to foot-lamberts.

fL=25×0.09290304=2.32258 fL\text{fL} = 25 \times 0.09290304 = 2.32258\ \text{fL}

How to Convert apostilbs to foot-lamberts

Move luminance values from metric apostilbs to US foot-lamberts in a few steps.

  1. Start with apostilbs: Take your luminance value, for example 25 asb.
  2. Multiply by 0.09290304: The apostilb-to-foot-lambert factor.
  3. Read the result: 25 × 0.09290304 = 2.32258 foot-lamberts.
  4. Reverse-check: Multiply foot-lamberts by 10.76391 to return to apostilbs.

apostilbs to foot-lamberts conversion table

apostilbs (asb)foot-lamberts (fL)
00
10.09290304
20.1858061
30.2787091
40.3716122
50.4645152
60.5574182
70.6503213
80.7432243
90.8361274
100.9290304
151.393546
201.858061
252.322576
302.787091
403.716122
504.645152
605.574182
706.503213
807.432243
908.361274
1009.290304
15013.93546
20018.58061
25023.22576
30027.87091
40037.16122
50046.45152
60055.74182
70065.03213
80074.32243
90083.61274
100092.90304
2000185.8061
3000278.7091
4000371.6122
5000464.5152
10000929.0304
250002322.576
500004645.152
1000009290.304
25000023225.76
50000046451.52
100000092903.04

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.

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 apostilb?

One apostilb equals 0.09290304 foot-lamberts, which is exactly the number of square feet in one square metre inverted—0.09290304 is the square-foot-to-square-metre area factor.

How do I convert apostilbs to foot-lamberts?

Multiply the apostilb value by 0.09290304. For example, 100 apostilbs equals 100 × 0.09290304 = 9.290304 foot-lamberts.

How do I convert foot-lamberts back to apostilbs?

Multiply foot-lamberts by 10.76391. So 5 foot-lamberts equals about 53.82 apostilbs.

Why is the factor the same as an area conversion?

Both units are 1/π diffuse-luminance units, so their ratio reduces to converting per-square-metre to per-square-foot, giving the 0.09290304 factor.

Where are foot-lamberts commonly used?

Foot-lamberts are standard in cinema and projection engineering for specifying screen brightness, such as the SMPTE target of about 14 fL for theater screens.

People also convert

asb to cd/m2asb to ntasb to sbasb to L

Complete apostilbs conversion table

asb
UnitResult
candelas per square metre (cd/m2)0.3183099 cd/m2
nits (nt)0.3183099 nt
stilbs (sb)0.00003183099 sb
lamberts (L)0.0001 L
foot-lamberts (fL)0.09290304 fL

Luminance conversions