1. What is a Projection Distance Calculator?

Definition: This calculator computes either the projection distance (\( T \)) or the focal length of the lens (\( f \)) based on the height of the frame of projection media (\( h \)) and the height of the image on the screen (\( H \)).

Purpose: It assists in setting up projection systems by determining the required throw distance or lens focal length for a desired image size.

2. How Does the Calculator Work?

The calculator uses the following formulas:

Projection Distance: \[ T = \frac{f \times H}{h} \]

Focal Length: \[ f = \frac{T \times h}{H} \]

Where:

• \( T \): Projection distance
• \( f \): Focal length of lens
• \( h \): Height of frame of projection media
• \( H \): Height of image on screen

Unit Conversions:

• Focal Length (\( f \)) and Frame Height (\( h \)): in, mm (1 mm = 0.0393701 in), cm (1 cm = 0.393701 in)
• Projection Distance (\( T \)) and Image Height (\( H \)): ft, m (1 m = 3.28084 ft), cm (1 cm = 0.0328084 ft)
• Output Units: in, ft, cm, m, yard (1 yard = 3 ft = 0.9144 m)

Steps:

• Select whether to calculate projection distance or focal length.
• Enter the required inputs and their units.
• Select the output unit for the result.
• All calculations are converted to meters internally for consistency, then to the selected output unit.
• Display the result in the chosen unit with 5 decimal places or scientific notation for extreme values.

3. Importance of Projection Distance Calculation

Calculating projection distance or focal length is crucial for:

• Image Quality: Ensures the projected image fits the screen without distortion.
• Setup Planning: Determines the correct projector placement or lens selection.
• Space Efficiency: Optimizes room layout for the projection setup.

4. Using the Calculator

Examples:

• Example 1 (Projection Distance): For \( f = 6 \, \text{in} \), \( h = 1 \, \text{in} \), \( H = 8 \, \text{ft} \), output unit ft:
  • \( T = \frac{6 \times 8}{1} = 48 \, \text{ft} \)
  • Display: \( 48.00000 \, \text{ft} \)
• Example 2 (Focal Length): For \( T = 20 \, \text{ft} \), \( h = 24 \, \text{mm} \), \( H = 3 \, \text{m} \), output unit in:
  • Convert inputs to meters: \( T = 6.096 \, \text{m} \), \( h = 0.024 \, \text{m} \), \( H = 3 \, \text{m} \)
  • \( f = \frac{6.096 \times 0.024}{3} \approx 0.04877 \, \text{m} = 1.92000 \, \text{in} \)
  • Display: \( 1.92000 \, \text{in} \)

5. Frequently Asked Questions (FAQ)

Q: What does projection distance (T) represent?
A: It is the throw distance from the projector to the screen, critical for proper image sizing.

Q: How is focal length (f) determined?
A: Focal length is calculated based on the desired projection distance, frame height, and image height, influencing the throw ratio.

Q: Can this be used for width-based calculations?
A: Yes, substitute width (\( w \) and \( W \)) into the formulas (\( T = \frac{f \times W}{w} \) or \( f = \frac{T \times w}{W} \)) for equivalent results.

6. Frame Sizes of Common Projection Media

Projection Media	Frame Size (inches)			Frame Size (metric)
	h	w	w/h	h	w
Standard 35 mm slide	0.902	1.346	1.49	22.9	34.2
2 x 2 super slide	1.496	1.496	1.00	38.0	38.0
126 (instamatic) slide	1.043	1.043	1.00	26.5	26.5
35 mm half-frame slide	0.626	0.902	1.44	15.9	22.9
2 1/4 x 2 1/4 slide	2.031	2.031	1.00	51.6	51.6
8 mm motion picture	0.129	0.172	1.33	3.28	4.37
Super 8	0.158	0.211	1.33	4.01	5.36
16 mm motion picture	0.284	0.380	1.33	7.21	9.65
35 mm motion picture	0.600	0.823	1.37	15.2	20.9
Overhead projector	7.5	10.0	1.33	191	254

For rectangular formats, unless it is known that slides always will be shown horizontally, screen size should be sized for the largest dimension.

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