Foot-candles (ft-cd) to Lux (lx) conversion

Converting between foot-candles and lux is a common task in lighting design and measurement. Here's a breakdown of the conversion process, some context, and examples.

Understanding the Conversion

Foot-candle (fc) and lux (lx) are both units of illuminance, which measures the amount of light falling on a surface.

• Foot-candle (fc): Defined as one lumen per square foot.
• Lux (lx): Defined as one lumen per square meter. This is the SI unit for illuminance.

The key to conversion lies in the relationship between square feet and square meters.

Conversion Formulas

• Foot-candles to Lux:

  $$\text{Lux} = \text{Foot-candles} \times 10.764$$

• Lux to Foot-candles:

  $$\text{Foot-candles} = \text{Lux} \div 10.764$$

Step-by-Step Conversion Instructions

Converting 1 Foot-candle to Lux:

1. Start with the value in foot-candles: 1 fc
2. Multiply by the conversion factor: $1 \text{ fc} \times 10.764 = 10.764 \text{ lx}$

Therefore, 1 foot-candle is equal to 10.764 lux.

Converting 1 Lux to Foot-candle:

1. Start with the value in lux: 1 lx
2. Divide by the conversion factor: $1 \text{ lx} \div 10.764 = 0.0929 \text{ fc}$

Therefore, 1 lux is approximately equal to 0.0929 foot-candles.

Interesting Facts and Laws

While there isn't a specific "law" tied directly to the foot-candle to lux conversion, the underlying principle relates to the inverse square law of light. This law states that the illuminance decreases proportionally to the square of the distance from the light source.

The inverse square law plays a crucial role in lighting design, influencing the necessary light source intensity and placement to achieve the desired illuminance levels.

Real-World Examples

Here are a few examples of illuminance levels in foot-candles and lux:

• Office Lighting: Typical office spaces aim for around 500 lux (approximately 46 foot-candles) to ensure adequate visibility for tasks.
• Reading: Reading requires about 400 lux, equivalent to around 37 foot-candles.
• Hospital examination room: According to IESNA(Illuminating Engineering Society of North America), an examination room require 1,000 lux and 93 foot-candles.
• Outdoor Full Sunlight: On a sunny day, illuminance can reach up to 100,000 lux (approximately 9290 foot-candles).
• Moonlight: On a clear night, moonlight provides around 1 lux (approximately 0.09 foot-candles).
• Street lighting Per IESNA standard, a roadway typically has an average maintained illuminance of 5 to 20 lux(0.46 to 1.85 foot-candles)

These examples demonstrate the range of illuminance levels encountered in everyday environments and highlight the importance of accurate conversion between lux and foot-candles in lighting design and assessment.

Sources

• IES - Illuminating Engineering Society

How to Convert Foot-candles to Lux

To convert Foot-candles (ft-cd) to Lux (lx), multiply the Foot-candle value by the conversion factor. Since Lux is the metric unit of illuminance, this converts the measurement into SI units.

1. Write down the conversion factor:
   The relationship between the two units is:

   $$1\ \text{ft-cd} = 10.76391\ \text{lx}$$

2. Set up the conversion formula:
   Use the formula:

   $$\text{Lux} = \text{Foot-candles} \times 10.76391$$

3. Substitute the given value:
   Insert $25$ for the Foot-candle value:

   $$\text{Lux} = 25 \times 10.76391$$

4. Perform the multiplication:

   $$25 \times 10.76391 = 269.09775$$

5. Result:

   $$25\ \text{ft-cd} = 269.09775\ \text{lx}$$

A quick way to check your work is to remember that Lux is larger in numeric value than Foot-candles, so the result should be greater than 25. For repeated conversions, keep the factor $10.76391$ handy.

What is the formula to convert Foot-candles to Lux?

To convert Foot-candles to Lux, multiply the Foot-candle value by the verified factor $10.76391$. The formula is: $lx = ft\text{-}cd \times 10.76391$. This works because $1\ ft\text{-}cd = 10.76391\ lx$.

How many Lux are in 1 Foot-candle?

There are $10.76391\ lx$ in $1\ ft\text{-}cd$. This is the standard conversion factor used for illumination measurements. It provides a direct way to compare imperial and metric lighting units.

Why do Foot-candles and Lux have different values?

Foot-candles and Lux both measure illuminance, but they are based on different area units. A Foot-candle uses square feet, while Lux uses square meters. Because of this difference, $1\ ft\text{-}cd$ equals $10.76391\ lx$.

Where is converting Foot-candles to Lux used in real life?

This conversion is commonly used in lighting design, photography, workplace safety, and building standards. For example, a light meter may show readings in Foot-candles, while project specifications require Lux. Converting between them helps ensure lighting levels meet the correct standard.

Can I convert Lux back to Foot-candles?

Yes, you can convert in the opposite direction by dividing the Lux value by $10.76391$. The reverse formula is: $ft\text{-}cd = lx \div 10.76391$. This is useful when a measurement is given in metric units but you need imperial units.

Does this conversion factor change depending on the type of light?

No, the conversion factor does not depend on the light source. Whether the light comes from LED, fluorescent, or daylight, the unit relationship remains $1\ ft\text{-}cd = 10.76391\ lx$. Only the measured illuminance changes, not the conversion itself.