Hyperfocal distance formula, with a calculator table in Excel

The hyperfocal distance formula

H = f² ÷ (N × c) + f

• f is the real focal length of the lens in mm.
• N is the f-number, for example 11 for f/11.
• c is the circle of confusion in mm: the largest blur spot that still looks sharp.

For 21 mm at f/11: 21² = 441, 441 ÷ (11 × 0.03) = 1,336.4 mm, plus 21 mm gives 1,357.4 mm, or 1.36 m. Many calculators drop the final + f, which gives 1.34 m. The difference is only the focal length itself and does not matter in the field.

A hyperfocal table in Excel

Put the focal lengths down column A and the f-numbers across row 3. One formula with mixed references fills the whole table: =($A4^2/(B$3*$B$1)+$A4)/1000. The $ before A keeps the focal length column fixed, the $ before 3 keeps the f-number row fixed, and $B$1 always points to the circle of confusion. Dividing by 1000 turns millimetres into metres.

The table shows how strongly H depends on the focal length, because f is squared: a 16 mm lens at f/22 is sharp from 0.20 m to infinity when focused at 0.40 m, while a 50 mm lens at f/8 needs to be focused at 10.47 m. To read one value, look it up with =INDEX(B4:E8,MATCH(B11,A4:A8,0),MATCH(B12,B3:E3,0)).

Worked example: hyperfocal table for 16–50 mm on full frame

The circle of confusion in B1, the f-numbers in row 3 and the focal lengths in column A are inputs (yellow). B4:E8 is one copied formula. Rows 11 to 18 plan a landscape shot with a 21 mm lens at f/11.

Worked example: hyperfocal table for 16–50 mm on full frame

	A	B	C	D	E
1	Circle of confusion c (mm)	0.030
2	Hyperfocal distance H (m)	f/8	f/11	f/16	f/22
3	f-number N →	8	11	16	22
4	16	1.08	0.79	0.55	0.40
5	21	1.86	1.36	0.94	0.69
6	28	3.29	2.40	1.66	1.22
7	35	5.14	3.75	2.59	1.89
8	50	10.47	7.63	5.26	3.84
9
10	Landscape plan	Value
11	Focal length (mm)	21
12	f-number	11
13	Hyperfocal distance H (m)	1.36
14	Sharp from (m), focused at H	0.68
15	Focus distance s (m)	0.90
16	Near limit at s (m)	0.54
17	Far limit at s (m)	2.67
18	Formula without + f (m)	1.34

Thin-lens approximations, distances in metres, full-frame circle of confusion 0.03 mm. Educational calculations, with no affiliation with any camera or lens maker.

Choosing the circle of confusion

The circle of confusion is a viewing standard, not a property of the lens. The traditional value for full frame is about 0.03 mm (some use 0.029 mm, the sensor diagonal ÷ 1500), based on a print of about 8 × 10 inches seen from normal viewing distance. Smaller sensors need a smaller c in proportion to the crop factor, roughly 0.02 mm for APS-C and 0.015 mm for Micro Four Thirds.

Because c is in the denominator, halving it doubles the hyperfocal distance. If you print large or check images at 100% on a high-resolution sensor, use a smaller c, or simply focus a little beyond the value in the table.

Focusing closer or farther than H

If you focus at a distance s instead of H, the sharp zone changes. A good approximation when s is much larger than the focal length:

• Near limit ≈ H × s ÷ (H + s)
• Far limit ≈ H × s ÷ (H − s), and infinity once s ≥ H

Focusing the 21 mm lens at 0.9 m, closer than H, gives a sharp zone from 0.54 m to 2.67 m: the foreground gets sharper, but the horizon is lost. Focusing at infinity is the opposite mistake: everything is sharp only from H, 1.36 m, onwards, and the near half of the zone is wasted. At exactly H, the near limit is H ÷ 2 and the far limit is infinity, the widest zone possible.

Why not just stop down to f/22?

A smaller aperture shortens the hyperfocal distance, but very small apertures soften the whole image through diffraction. On full frame, many landscape photographers prefer to stay around f/8 to f/11 and use the hyperfocal distance of that aperture, rather than f/22 everywhere. Compare the f/11 and f/22 columns of the table to see what you gain in depth.

Hyperfocal distance and depth of field

The hyperfocal distance is a special case of depth of field: the focus distance at which the far limit just reaches infinity. The general near and far limits use the same ingredients, f, N, c and the focus distance. The optics behind the focal length itself, how a lens forms an image at a given distance, are covered in the thin lens equation guide.

Common mistakes

• Mixing millimetres and metres. Keep f and c in mm inside the formula and convert the result once at the end.
• Using the full-frame circle of confusion on a smaller sensor. Divide 0.03 mm by the crop factor, about 0.02 mm for APS-C.
• Using the equivalent focal length. Use the real focal length printed on the lens with the smaller c of your sensor, not the full-frame equivalent.
• Focusing at infinity for landscapes. Everything closer than H is then soft. Focus at H to start the sharp zone at H ÷ 2.
• Treating "acceptably sharp" as pixel-sharp. The result depends on the chosen c. For large prints, use a smaller c.