How to Calculate Depth of Field

What depth of field is

A lens focuses exactly at one distance. Points in front of and behind that plane spread into small blur circles, and while those circles stay smaller than a chosen size, the circle of confusion, they still read as sharp. Depth of field is the span between the nearest and farthest distances where that holds.

Four things set it: the focal length, the stop, the focus distance, and the circle of confusion you allow, which in practice comes from the format and how big the picture will be seen. Sharpness also falls off gradually rather than at a hard edge, so the limits are a planning tool, not a guarantee. The circle of confusion guide explains where that blur budget comes from.

The depth of field formula

The standard thin-lens formulas start from the hyperfocal distance H, the closest focus at which the far limit reaches infinity, and then give each limit directly. All lengths are in millimeters.

In that example 10.4cm of the zone sits in front of the subject and 11.6cm behind. The Cinema Calculations Handbook has the short approximation, DoF ≈ 2 × N × c × s² ÷ f², which is close as long as you are well inside the hyperfocal distance and shows the relationships at a glance. The free depth of field calculator runs both formulas above in your browser, in feet or meters.

What changes depth of field

Read the approximation above and the four levers fall out. Two of them act as squares, which is why a lens change or a step closer changes the focus puller's life far more than a stop does.

• Distance (squared). The same 50mm at T2.8 holds 7.7cm at 1.2m, 22cm at 2m and 90cm at 4m. Double the distance and you get roughly four times the depth.
• Focal length (inverse square). At 3m and T2.8, a 25mm holds 2.25m, a 50mm 50cm and a 100mm 12cm. Double the focal length and you keep about a quarter.
• Stop (in proportion). The 50mm at 3m goes 36cm at T2, 50cm at T2.8, 72cm at T4 and 102cm at T5.6: about 1.4 times per stop, so two stops roughly double it.
• Circle of confusion (in proportion). Halve the blur you will accept, from 0.025mm to 0.0125mm, and the 50cm at 3m becomes 25cm.

Sensor size and depth of field

A larger sensor on its own does not shrink depth of field; it allows a larger circle of confusion, which adds some. What shrinks it is the longer lens you fit to hold the same framing. The net effect, for the same shot at the same stop, is shallower focus on the bigger format.

The Focal Length Match calculator does the first half of this, the lens that holds the framing on another sensor. The crop factor guide covers that ratio in detail, and the sensor size chart gives the diagonal, and so the circle of confusion, for each camera's recording modes. For the second half, enter each format's lens, stop and circle of confusion in the free depth of field calculator.

In front of and behind the subject

The old rule says a third of the depth of field falls in front of the subject and two-thirds behind. The formulas say the split depends on how far you are from the hyperfocal distance: the ratio of back to front is (H + s) ÷ (H − s), which is 2 only at s = H ÷ 3. Close up, the zone is almost evenly split.

For the close and medium shots where focus is hardest, plan on an even split, not a third and two-thirds. If anything, an AC who leans a mark slightly behind the subject on a close-up is betting on an advantage that is not there.

Depth of field charts

Super 35 with the 0.025mm circle of confusion that cine lens makers use for 35mm depth of field tables. For full frame at 0.030mm, the same lens and stop give about a fifth more depth; at a different format, use the format's own value from the circle of confusion table.

Total depth of field at 3m (9′10″)

Near and far limits in feet at T2.8

Hyperfocal distances for each format, and the near limit when you focus there, are in the hyperfocal distance charts.

Using the numbers on set

A 1st AC rarely calculates depth of field mid-take. The numbers matter in prep and at the blocking rehearsal, when there is still time to change the plan.

• Know the budget for the shot. At the rehearsal, check the lens, stop and marks against the depth you have. A 75mm at T2 focused at 1.7m (5′7″) on Super 35 holds about 5cm, so an actor who drifts a hand's width off the mark is soft: ask for a firmer mark, a reference, or a stop. The exposure triangle guide shows where the extra light can come from.
• Measure from the focal plane. Tape and laser measurements run from the sensor mark (⦶) on the camera body, the same reference the lens's focus scale uses.
• Spend the depth where it matters. On a close-up the zone is evenly split, so set the mark on the eyes, not the tip of the nose or the ear.
• Plan two subjects, don't guess. Holding two people at different distances has an exact answer for the focus point and the stop; see split focus.
• Judge on a big, sharp monitor. A 7-inch on-board screen hides softness that a theater screen shows. The calculator says what the optics allow; the monitor, zoomed in, says whether you hit it.

Questions

Next step: run your own lens, stop and distance. CineMath's Depth of Field calculator gives the near and far limits, the hyperfocal distance and a split-focus plan in feet or meters, with a preset circle of confusion for each format. The free web version does the same in your browser.