This calculator helps determine crucial camera settings like focal length, field of view, and depth of field based on your camera's sensor size and lens specifications.
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Understanding Camera Math
Photography and videography involve a fascinating interplay of physics and mathematics. Understanding the core concepts behind your camera's operation can significantly improve your creative control and technical output. This calculator helps demystify some of these key relationships.
Key Concepts:
Sensor Size (Width & Height): The dimensions of the digital sensor inside your camera. Different sensor sizes (e.g., Full Frame, APS-C, Micro Four Thirds) affect the effective focal length and field of view.
Focal Length: The distance from the optical center of the lens to the image sensor when the lens is focused at infinity. It primarily determines the magnification and field of view. Shorter focal lengths provide a wider field of view (wide-angle), while longer focal lengths provide a narrower field of view and greater magnification (telephoto).
Aperture (f-stop): The physical opening within the lens that controls the amount of light reaching the sensor. It is expressed as an f-number (e.g., f/1.8, f/5.6). A smaller f-number indicates a larger aperture opening, allowing more light and resulting in a shallower depth of field. A larger f-number means a smaller aperture opening, less light, and a deeper depth of field.
Subject Distance: The distance between the front of the lens and the subject being photographed. This is crucial for calculating depth of field.
Circle of Confusion (CoC): The maximum acceptable blur diameter on the sensor that is still perceived as a sharp point by the human eye at a standard viewing distance. It's used to calculate the hyperfocal distance and depth of field. CoC values vary based on sensor size and viewing conditions.
Calculations Performed:
1. Equivalent Focal Length (Crop Factor):
This calculation shows how a lens's field of view on a smaller sensor compares to a standard 35mm (Full Frame) sensor. While not directly calculated here as a standalone number, the sensor dimensions relative to focal length implicitly determine the field of view.
2. Field of View (Horizontal & Vertical):
The Field of View (FoV) is the extent of the scene that is captured by the camera. It is calculated using the sensor dimensions and the focal length. The formulas use trigonometry (arctangent) to determine the angles.
DoF refers to the range of distances in a scene that appear acceptably sharp in an image. It's influenced by focal length, aperture, and subject distance.
Far Limit of DoF:(Subject Distance * (Hyperfocal Distance - Subject Distance)) / (Hyperfocal Distance - Subject Distance)
Total DoF:Far Limit - Near Limit
4. Hyperfocal Distance:
The closest distance at which a lens can be focused while maintaining acceptable sharpness to infinity. Focusing at the hyperfocal distance maximizes the depth of field.
Hyperfocal Distance:(Focal Length^2) / (Aperture * Circle of Confusion * 1000) (Note: conversion to meters included in the calculation logic)
Use Cases:
Cinematography: Determining how much of the scene will be in focus for a particular shot, crucial for artistic intent and ensuring subjects are sharp.
Landscape Photography: Calculating the hyperfocal distance to ensure maximum sharpness from foreground elements to distant horizons.
Portrait Photography: Understanding how aperture and distance affect the background blur (bokeh) and subject isolation.
Product Photography: Controlling the depth of field to showcase specific product details while keeping the rest sharp or blurred as desired.
Understanding Lenses: Comparing how different focal lengths and apertures affect the final image's perspective and sharpness.
By inputting your camera's sensor dimensions, lens specifications, and subject distance, this calculator provides valuable insights into the optical principles at play, empowering you to make more informed creative decisions.
// JavaScript for Camera Math Calculator
function calculateCameraMath() {
// Get input values
var sensorWidth = parseFloat(document.getElementById("sensorWidth").value);
var sensorHeight = parseFloat(document.getElementById("sensorHeight").value);
var focalLength = parseFloat(document.getElementById("focalLength").value);
var aperture = parseFloat(document.getElementById("aperture").value);
var subjectDistance = parseFloat(document.getElementById("subjectDistance").value);
var circleOfConfusion = parseFloat(document.getElementById("circleOfConfusion").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
// Input validation
if (isNaN(sensorWidth) || sensorWidth <= 0 ||
isNaN(sensorHeight) || sensorHeight <= 0 ||
isNaN(focalLength) || focalLength <= 0 ||
isNaN(aperture) || aperture <= 0 ||
isNaN(subjectDistance) || subjectDistance <= 0 ||
isNaN(circleOfConfusion) || circleOfConfusion 0) {
// Near limit of DoF
var numeratorNear = subjectDistance * (hyperfocalDistanceMeters – subjectDistance);
var denominatorNear = hyperfocalDistanceMeters + subjectDistance – (2 * subjectDistance);
if (denominatorNear !== 0) { // Avoid division by zero
dofNearLimitMeters = numeratorNear / denominatorNear;
} else {
dofNearLimitMeters = 0; // Should not happen with typical values but safe check
}
// Far limit of DoF
var numeratorFar = subjectDistance * (hyperfocalDistanceMeters – subjectDistance);
var denominatorFar = hyperfocalDistanceMeters – subjectDistance;
if (denominatorFar !== 0) { // Avoid division by zero
dofFarLimitMeters = numeratorFar / denominatorFar;
} else {
dofFarLimitMeters = Infinity; // If denominator is 0, far limit is infinity
}
// Total DoF
if (dofFarLimitMeters !== Infinity && dofNearLimitMeters >= 0) {
totalDofMeters = dofFarLimitMeters – dofNearLimitMeters;
} else {
totalDofMeters = Infinity;
}
}
// Format results
var formattedHFOV = horizontalFovDeg.toFixed(2);
var formattedVFOV = verticalFovDeg.toFixed(2);
var formattedHFD = hyperfocalDistanceMeters.toFixed(2);
var formattedNearDoF = dofNearLimitMeters.toFixed(2);
var formattedFarDoF = (dofFarLimitMeters === Infinity) ? "Infinity" : dofFarLimitMeters.toFixed(2);
var formattedTotalDoF = (totalDofMeters === Infinity) ? "Infinity" : totalDofMeters.toFixed(2);
// Display results
resultDiv.innerHTML = `
Field of View: ${formattedHFOV}° (H) / ${formattedVFOV}° (V)
Hyperfocal Distance: ${formattedHFD} m
Depth of Field: ${formattedNearDoF} m (Near) to ${formattedFarDoF} m (Far)