# Optomath: Photographic Equations

Full version of Optomath is available for download in PDF format.

Additional sheet included for usage with Maple Software.

**35mm Focal Length Multiplier**

**m _{f35} = **

**d**

_{35}**/ d**

_{i}

*=*√(36

^{2}+ 24

^{2}) / d

_{i}= √1872 / d

_{i}

where: | |

m_{f35} |
is the 35mm focal length multiplier |

d_{35} |
is the diagonal of the 35mm (135) format, mm |

d_{i} |
is the diagonal of the initial image, mm |

**35mm Equivalent Focal Length**

**f _{35} = f_{i} * m_{f35}**

where: | |

f_{35} |
is the 35mm equivalent focal length, mm |

f_{i} |
is the initial focal length, mm |

m_{f35} |
is the 35mm focal length multiplier |

**Circle of Confusion**

**c = d / x**

where: | |

c |
is the circle of confusion, mm |

d |
is the image diagonal, mm |

x |
is the divisor |

divisors:

1500 (used by Zeiss, we recommend)

1730 (used by Leica)

1300 (used by Nikon)

On the web you’ll found many site says d/1730 is the “Zeiss Formula”, but that’s a bullshit.

Read the official Zeiss publication about depth of field & circle of confusion on page 3 here.

**Depth of Field Equations**

Hyperfocal distance, near distance of acceptable sharpness, and far distance of acceptable sharpness are calculated using the following equations (from Greenleaf, Allen R., *Photographic Optics*, The MacMillan Company, New York, 1950, pp. 25-27):

**Hyperfocal distance:**

**Near distance of acceptable sharpness:**

**Far distance of acceptable sharpness:**

where: | |

H |
is the hyperfocal distance, mm |

f |
is the lens focal length, mm |

s |
is the focus distance, mm |

D_{n} |
is the near distance of acceptable sharpness, mm |

D_{f} |
is the far distance of acceptable sharpness, mm |

N |
is the f-number, f-stop |

c |
is the circle of confusion, mm |

f-number is calculated by the definition *N = 2 ^{i/2} , *where

*i = 1, 2, 3,…*for

*f/1.4, f/2, f/2.8,…*

Calculations using these equations must use consistent units. When focal length and circle of confusion have units of millimeters, the calculated hyperfocal distance will have units of millimeters.

To convert to feet, divide *H* by 304.8. To convert to meters, divide *H* by 1000.

**Angle of View (Field of View)**

**α**** = 2*arctan(d/2f) * (180/Pi)
**

where: | |

α | is the angle of view, degree |

d |
is the image diagonal, mm |

f |
is the focal length, mm |

*this formula gives results in degrees.*

This formula presumes lenses without distortion. These calculations don’t apply to fisheye lenses.

Different fisheyes use different projections, so different formulas apply to different fisheye lenses.

source 1, source 2

## About this entry

You’re currently reading “Optomath: Photographic Equations,” an entry on Pixelfarmize

- Published:
- April 28, 2009 / 10:37

- Category:
- Analog, Digital, Techniques

- Tags:
- angle of view, aov, circle of confusion, coc, depth of field, dof, equation, equivalent, field of view, fov, math, multiplier, optic, opto, photography, science

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