Canon PowerShot SD870 IS vs. Canon PowerShot G7 X

Diagonal is calculated by the use of Pythagorean theorem:

Diagonal = √

w² + h²

where w = sensor width and h = sensor height

The diagonal of SD870 IS sensor is not 1/2.5 or 0.4" (10.2 mm) as you might expect, but approximately two thirds of that value - 7.19 mm. If you want to know why, see sensor sizes.

w = 5.75 mm
h = 4.32 mm

Diagonal = √

5.75² + 4.32²

= 7.19 mm

w = 13.20 mm
h = 8.80 mm

Diagonal = √

13.20² + 8.80²

= 15.86 mm

Surface area is calculated by multiplying the width and the height of a sensor.

Width = 5.75 mm
Height = 4.32 mm

Surface area = 5.75 × 4.32 = 24.84 mm²

Width = 13.20 mm
Height = 8.80 mm

Surface area = 13.20 × 8.80 = 116.16 mm²

Pixel pitch is the distance from the center of one pixel to the center of the next measured in micrometers (µm). It can be calculated with the following formula:

Pixel pitch =	sensor width in mm	× 1000
	sensor resolution width in pixels

Sensor width = 5.75 mm
Sensor resolution width = 3262 pixels

Pixel pitch =	5.75	× 1000	= 1.76 µm
	3262

Sensor width = 13.20 mm
Sensor resolution width = 5505 pixels

Pixel pitch =	13.20	× 1000	= 2.4 µm
	5505

The area of one pixel can be calculated by simply squaring the pixel pitch:

You could also divide sensor surface area with effective megapixels:

Pixel area =	sensor surface area in mm²
	effective megapixels

Pixel pitch = 1.76 µm

Pixel area = 1.76² = 3.1 µm²

Pixel pitch = 2.4 µm

Pixel area = 2.4² = 5.76 µm²

Pixel density can be calculated with the following formula:

Pixel density =  (	sensor resolution width in pixels	)² / 1000000
	sensor width in cm

One could also use this formula:

Pixel density =	effective megapixels × 1000000	/ 10000
	sensor surface area in mm²

Sensor resolution width = 3262 pixels
Sensor width = 0.575 cm

Pixel density = (3262 / 0.575)² / 1000000 = 32.18 MP/cm²

Sensor resolution width = 5505 pixels
Sensor width = 1.32 cm

Pixel density = (5505 / 1.32)² / 1000000 = 17.39 MP/cm²

Sensor resolution is calculated from sensor size and effective megapixels. It's slightly higher than maximum (not interpolated) image resolution which is usually stated on camera specifications. Sensor resolution is used in pixel pitch, pixel area, and pixel density formula. For sake of simplicity, we're going to calculate it in 3 stages.

1. First we need to find the ratio between horizontal and vertical length by dividing the former with the latter (aspect ratio). It's usually 1.33 (4:3) or 1.5 (3:2), but not always.

2. With the ratio (r) known we can calculate the X from the formula below, where X is a vertical number of pixels:

(X × r) × X = effective megapixels × 1000000    →

X = √  effective megapixels × 1000000 r

3. To get sensor resolution we then multiply X with the corresponding ratio:

Resolution horizontal: X × r
Resolution vertical: X

Sensor width = 5.75 mm
Sensor height = 4.32 mm
Effective megapixels = 8.00

r = 5.75/4.32 = 1.33

X = √  8.00 × 1000000  = 2453 1.33

Resolution horizontal: X × r = 2453 × 1.33 = 3262
Resolution vertical: X = 2453

Sensor resolution = 3262 x 2453

Sensor width = 13.20 mm
Sensor height = 8.80 mm
Effective megapixels = 20.20

r = 13.20/8.80 = 1.5

X = √  20.20 × 1000000  = 3670 1.5

Resolution horizontal: X × r = 3670 × 1.5 = 5505
Resolution vertical: X = 3670

Sensor resolution = 5505 x 3670

Crop factor or focal length multiplier is calculated by dividing the diagonal of 35 mm film (43.27 mm) with the diagonal of the sensor.

Crop factor =	43.27 mm
	sensor diagonal in mm

Sensor diagonal in mm = 7.19 mm

Crop factor =	43.27	= 6.02
	7.19

Sensor diagonal in mm = 15.86 mm

Crop factor =	43.27	= 2.73
	15.86

Equivalent aperture (in 135 film terms) is calculated by multiplying lens aperture with crop factor (a.k.a. focal length multiplier).

Crop factor = 6.02
Aperture = f2.8 - f5.8

35-mm equivalent aperture = (f2.8 - f5.8) × 6.02 = f16.9 - f34.9

Crop factor = 2.73
Aperture = f1.8 - f2.8

35-mm equivalent aperture = (f1.8 - f2.8) × 2.73 = f4.9 - f7.6