Total Lumen Output Calculator

Illuminance (E₂):

Initial Distance (d₂):

Reference Distance (d₁):

Solid Angle Blocked (α): degrees

Irradiance at d₁ (E₁):

lm/m²

Luminance per Steradian:

lm/sr

Solid Angle (W):

Total Lumen Output:

1. What is the Lumen Output Calculator?

Definition: This calculator determines the total lumen output of a light bulb based on measured illuminance, distances, and the solid angle blocked by the base, assuming an isotropic point source.

Purpose: It is used in lighting design and photometry to assess the total light output of a bulb with partial blocking.

2. How Does the Calculator Work?

The calculator follows these steps:

Calculate irradiance at a reference distance using the Inverse Square Law: \( E_1 = (d_2 / d_1)^2 * E_2 \)
Convert irradiance to luminance per steradian: \( 1 \, \text{m}^2/\text{sr} \) at the reference distance
Calculate solid angle blocked: \( W = 2\pi[1 - \cos((360 - \alpha) / 2)] \)
Calculate total lumen output: \( \text{Lumen Output} = \text{Luminance per sr} * \text{Solid Angle} \)

Where:

\(E_1\): Irradiance at reference distance (lm/m²)
\(E_2\): Initial illuminance (lux)
\(d_1\): Reference distance (m)
\(d_2\): Initial distance (m)
\(\alpha\): Solid angle blocked (degrees)
\(W\): Solid angle (sr)

Unit Conversions:

Illuminance: lux, lm/m², lm/cm², fc, lm/ft² (converted to lux)
Distance: m, cm, mm, ft, in (converted to m)
Solid Angle: degrees (converted to sr)

Steps:

Enter the illuminance (E₂) and select its unit.
Enter the initial distance (d₂) and select its unit.
Enter the reference distance (d₁) and select its unit.
Enter the solid angle blocked (α) in degrees.
Click "Calculate" to determine irradiance, luminance per steradian, solid angle, and total lumen output.

3. Importance of Lumen Output Calculation

Understanding lumen output is crucial for:

Lighting Design: Ensuring adequate light levels for specific applications.
Energy Efficiency: Evaluating the performance of light sources.
Product Specification: Providing accurate data for bulb manufacturers.

4. Using the Calculator

Examples:

Example 1: Illuminance = 22.0 lux at 3.162 m, reference distance = 1.0 m, solid angle = 30°:
- \(E_1 = (3.162 / 1.0)^2 * 22.0 = 220 \, \text{lm/m}^2\)
- Luminance per sr = 220 lm/sr
- \(W = 2\pi[1 - \cos(30^\circ / 2)] = 12.35 \, \text{sr}\)
- Total Lumen Output = 220 * 12.35 = 2717 lm

5. Frequently Asked Questions (FAQ)

Q: What is an isotropic point source?
A: A source that emits light equally in all directions, except where blocked.

Q: Why is the solid angle important?
A: It accounts for the portion of the light blocked by the lamp base, affecting total output.