Complete Guide to Filmmaking Math

Updated

The everyday arithmetic of production and post: aspect ratios and letterbox bars, frame rates, timecode and drop-frame, film footage, file sizes, bitrates and transfer times.

30 min readIntermediate
  • Production & Post
  • Timecode
  • Film Footage
  • Storage & Data
On this page

Introduction to Filmmaking Math

Picture shape, frame rate, timecode, film footage, file size and transfer time: the arithmetic of production and post. Each section gives the formula, a worked example and, where it helps, a reference table. For a full storage budget, see the storage planning guide.

Aspect Ratio Calculations

The aspect ratio is the picture's width divided by its height. Most aspect-ratio math is working out how a picture of one shape sits inside a frame of another: how many lines of picture, how wide the bars, how much is lost to a crop.

Basic Aspect Ratio Formula
Aspect Ratio = Width ÷ Height

Works in pixels, millimeters or any other unit, as long as both sides use the same one.

Where

Width
Horizontal dimension in pixels, millimeters, or any unit
Height
Vertical dimension in the same unit as width

Example: 4K UHD Aspect Ratio

Calculation:
3840 ÷ 2160 = 1.778
Result:
16:9 (or 1.78:1)

Letterboxing and Pillarboxing

A picture wider than the frame gets bars top and bottom (letterbox); a narrower one gets bars at the sides (pillarbox). Round the picture to an even number of lines or pixels so the bars match. The free aspect ratio calculator works out the bars in your browser.

Letterbox Bar Height
Bar Height = (Frame Height − Frame Width ÷ Picture Ratio) ÷ 2

The height of each black bar when a wider picture fills the width of the frame.

Where

Frame Height
Height of the delivery frame(pixels)
Frame Width
Width of the delivery frame(pixels)
Picture Ratio
Aspect ratio of the picture, such as 2.39(ratio)

Example: 2.39:1 picture in a 1920 × 1080 frame

Calculation:
1920 ÷ 2.39 = 803.3, rounded to 804 lines; (1080 − 804) ÷ 2 = 138
Result:
138-pixel bars top and bottom around a 1920 × 804 picture
Pillarbox Bar Width
Bar Width = (Frame Width − Frame Height × Picture Ratio) ÷ 2

The width of each side bar when a narrower picture fills the height of the frame.

Where

Frame Width
Width of the delivery frame(pixels)
Frame Height
Height of the delivery frame(pixels)
Picture Ratio
Aspect ratio of the picture, such as 1.33(ratio)

Example: 4:3 archive footage in a 1920 × 1080 frame

Calculation:
1080 × 4 ÷ 3 = 1440; (1920 − 1440) ÷ 2 = 240
Result:
240-pixel bars either side of a 1440 × 1080 picture

Case study

One Scope Master, Three Deliverables

  • Documentary
  • Intermediate
  • Worked example

Scenario

A documentary is finished at 2.39:1 in a UHD timeline. It needs a 16:9 UHD streaming file, an HD version and a 1:1 cut-down for social media.

Challenge

Work out the picture size and bars for each version, and where the square crop should come from.

Solution

  1. Set the picture height of the scope master inside the UHD frame
  2. Letterbox the master into 16:9 for streaming and HD
  3. Take the square crop from the highest-resolution master, so it is scaled down rather than up
  4. Reframe the square crop shot by shot, since a center crop throws away more than half of a scope frame

The numbers

  • UHD picture: 3840 ÷ 2.39 = 1606.7, rounded to 1608 lines
  • 16:9 UHD bars: (2160 − 1608) ÷ 2 = 276 lines top and bottom
  • HD version: 1920 × 804 picture with 138-line bars
  • 1:1 from the UHD master: 1608 × 1608 crop scaled to 1080 × 1080 (0.67×, a downscale); from the HD master the 804 × 804 crop would need a 1.34× upscale
  • A square crop keeps 1608 ÷ 3840 = 42% of the frame width

Result

All three versions come from the one scope master, with the social cut scaled down from UHD rather than up from HD.

Key takeaways

  • Round letterboxed pictures to an even number of lines
  • Crop social versions from the highest-resolution master
  • A square crop of a scope frame needs reframing, not a fixed center crop

Frame Rate Mathematics

Frame rate sets motion rendering, running time and broadcast compatibility. The arithmetic matters most when footage is played at a rate other than the one it was shot at: slow motion, and conforms between 24, 25 and 30fps. The frame rates guide explains 23.976 vs 24, and the free speed change calculator gives the speed and running time of a conform in your browser.

Running Time After a Frame Rate Conform
New Duration = Original Duration × (Original FPS ÷ Target FPS)

When every frame is kept and simply played at a new rate, running time and audio pitch change. (A standards conversion that blends or repeats frames keeps the running time instead.)

Where

Original Duration
Running time at the original rate(minutes)
Original FPS
Rate the material was made at(fps)
Target FPS
Rate it will play at(fps)

Example: 24fps feature played at 25fps for a 50Hz broadcaster

Calculation:
100 min × (24 ÷ 25) = 96 min
Result:
Runs 4% faster and 4 minutes shorter, with audio about 0.7 semitone sharp unless pitch-corrected

Standard Frame Rates

RateExact ValueWhere It Is Used
24fps24Cinema projection and DCPs
23.976fps24000/1001Film-style production for 60Hz regions, streaming and HD video
25fps25Television and production in 50Hz regions (Europe, Australia and others)
29.97fps30000/1001Television in 60Hz regions (North America, Japan and others)
50 and 59.94fps50, 60000/1001Sports, live production, 720p and 1080p broadcast
48, 60 and 120fpsexactHigh-frame-rate cinema and high-speed capture
Slow Motion Frame Rate Calculation
Playback Speed % = (Playback FPS ÷ Capture FPS) × 100

The playback speed when every captured frame is played at the timeline rate.

Where

Playback FPS
Timeline or playback frame rate (usually 24, 25 or 30)(fps)
Capture FPS
Frame rate used during filming(fps)

Example: Capturing at 120fps, playing back at 24fps

Calculation:
(24 ÷ 120) × 100 = 20%
Result:
5x slower than real time (20% speed)

Timecode Calculations

Timecode (SMPTE ST 12-1) labels every frame as HH:MM:SS:FF. All timecode arithmetic works the same way: convert to a frame count, do the math, convert back.

Timecode to Frame Number
Frame Number = (H×3600 + M×60 + S) × FPS + F

Convert non-drop-frame timecode (HH:MM:SS:FF) to an absolute frame count.

Where

H
Hours
M
Minutes
S
Seconds
F
Frames
FPS
Timecode frame rate (24, 25 or 30)

Example: Converting 01:23:45:12 at 24fps

Calculation:
(1×3600 + 23×60 + 45) × 24 + 12 = 5,025 × 24 + 12 = 120,612
Result:
Frame number 120,612
Timecode Addition
Total Frames = Frame₁ + Frame₂, then convert back to timecode

Add two timecodes by converting to frames, adding, then converting back.

Example: Adding 00:05:30:15 + 00:02:45:08 at 25fps

Calculation:
8,265 + 4,133 = 12,398 frames = 495 seconds + 23 frames
Result:
00:08:15:23

Drop-Frame Timecode

At 29.97fps, non-drop timecode counts 30 labels a second for only 29.97 real frames, so it falls behind the clock by 3.6 seconds an hour. Drop-frame timecode (written with a semicolon, 01:00:00;00) skips the labels ;00 and ;01 at the start of every minute except minutes 00, 10, 20, 30, 40 and 50. No picture is dropped, only numbers. That removes 18 labels every 10 minutes, so ten minutes of drop-frame timecode is exactly 18,000 − 18 = 17,982 frames, which is 10 minutes of real time to within a fraction of a frame. The free timecode calculator does drop-frame math in your browser.

Drop-Frame Timecode to Frame Number (29.97fps)
Frame Number = (H×3600 + M×60 + S) × 30 + F − 2 × (Total Minutes − ⌊Total Minutes ÷ 10⌋)

Total Minutes = H × 60 + M. At 59.94fps use 60 and drop 4 labels instead of 2. 23.976fps has no drop-frame timecode.

Where

H, M, S, F
The drop-frame timecode fields
Total Minutes
H × 60 + M(minutes)

Example: 01:00:00;00 at 29.97fps

Calculation:
3600 × 30 − 2 × (60 − 6) = 108,000 − 108 = 107,892
Result:
Frame 107,892, which is one hour of real time: 107,892 ÷ 29.97 = 3,600 s

Film Footage Calculations

Film is measured in feet and frames. 35mm and 65mm stock both have 64 perforations per foot, so the frames per foot depend on how many perforations each frame uses; 16mm has 40 frames per foot. The free film footage calculator converts feet to running time and back in your browser.

Footage, Frames and Running Time
Running Time (s) = Feet × Frames per Foot ÷ FPS

Turn it around for stock: Feet = Running Time × FPS ÷ Frames per Foot.

Where

Feet
Length of film(feet)
Frames per Foot
16 for 35mm 4-perf, 40 for 16mm (table below)(frames)
FPS
Camera speed(fps)

Example: A 1,000ft roll of 35mm 4-perf at 24fps

Calculation:
1000 × 16 ÷ 24 = 666.7 seconds
Result:
About 11 minutes 7 seconds per roll (90 feet a minute)
FormatPerfs per FrameFrames per FootFeet per Minute at 24fpsRunning Time per Roll at 24fps
35mm 4-perf416901,000ft: 11.1 min
35mm 3-perf321⅓67.51,000ft: 14.8 min
35mm 2-perf232451,000ft: 22.2 min
16mm and Super 1614036400ft: 11.1 min
65mm 5-perf512.8112.51,000ft: 8.9 min

Storage & File Size Mathematics

File size is bitrate multiplied by time. Everything on this page uses decimal units (1 GB = 1,000,000,000 bytes), as drive makers and CineMath's Data & Storage calculator do; your operating system may show binary gigabytes, which read about 7% smaller.

Basic Storage Calculation
File Size (GB) = Bitrate (Mbps) × Duration (minutes) ÷ 133.33

133.33 is 8 bits per byte × 1,000 MB per GB ÷ 60 seconds per minute.

Where

Bitrate
Total bitrate, video plus audio(Mbps)
Duration
Content duration(minutes)

Example: 2-hour film at 50 Mbps

Calculation:
(50 × 120) ÷ 133.33 = 45 GB
Result:
45 GB
Production Storage Formula
Total Storage = Runtime × Shooting Ratio × GB per Hour × Copies + Working Space

Camera originals are the big number. Multiply by the number of copies you keep, then add space for proxies, renders and exports on the working drives.

Where

Runtime
Finished running time(hours)
Shooting Ratio
Footage shot per minute used: about 5:1 to 10:1 for commercials, 8:1 to 15:1 for scripted drama, 15:1 to 30:1 or more for documentary
GB per Hour
Storage per hour of the recording codec(GB/h)
Copies
Number of copies of the originals you keep (usually 2-3)
Working Space
Proxies, caches, renders and exports(GB)

Example: 2-hour feature, 10:1 ratio, UHD ProRes 422 HQ (318 GB/h), 3 copies

Calculation:
2 × 10 × 318 = 6,360 GB of originals; × 3 copies = 19,080 GB
Result:
About 19 TB before working space

Case study

Independent Film Storage Plan

  • Independent Feature
  • Intermediate
  • Worked example

Scenario

An independent feature with 90 minutes of finished running time, shot on two cameras, with editing on a laptop.

Challenge

How much storage does the shoot need, and how should it be split across drives?

Solution

  1. Estimate an 8:1 shooting ratio: 720 minutes of footage across both cameras
  2. Record ProRes 422 HQ at 1080p 29.97fps: 220 Mbps (Apple ProRes white paper)
  3. Keep three copies of the originals: 3-2-1 (3 copies, 2 kinds of media, 1 off site)
  4. Make ProRes Proxy files (45 Mbps at 1080p 29.97) for the edit

The numbers

  • Originals: 720 min × 220 Mbps ÷ 133.33 = 1,188 GB
  • Three copies of the originals: 1,188 × 3 = 3,564 GB
  • ProRes Proxy: 720 min × 45 Mbps ÷ 133.33 = 243 GB
  • Per drive: 1,188 GB of originals, plus 243 GB of proxies on the edit drive, leaves headroom on 2 TB drives; 4 TB drives allow for reshoots

Result

Three 4 TB drives, one per copy, hold the whole shoot with room to spare, and the proxies fit on the laptop's internal drive.

Key takeaways

  • Storage scales with minutes shot, not with finished running time
  • Plan for at least three copies of camera originals
  • Proxies at 45 Mbps are a fifth the size of 220 Mbps originals and edit smoothly on modest machines

Bitrate Calculations

Run the storage formula backwards to find the bitrate that hits a file size, then check it against the platform's own recommendations. The free bitrate calculator works it out either way in your browser.

Target Bitrate Formula
Bitrate (Mbps) = (Target File Size in GB × 133.33) ÷ Duration in minutes

The result is the total. Subtract the audio bitrate to get the video bitrate to set in the encoder.

Where

Target File Size
Desired final file size(GB)
Duration
Content duration(minutes)

Example: 2 GB file for a 30-minute episode

Calculation:
(2 × 133.33) ÷ 30 = 8.89 Mbps total; minus 0.32 Mbps of AAC audio
Result:
Set the video to about 8.5 Mbps

Published Bitrate Figures

What each figure means differs: YouTube publishes upload recommendations, Netflix publishes the connection speed it needs, and DCI and ATSC set hard limits.

PlatformFigureWhat It Is
YouTube, 2160p SDR35–45 Mbps (24–30fps), 53–68 Mbps (48–60fps)Recommended upload bitrate
YouTube, 1080p SDR8 Mbps (24–30fps), 12 Mbps (48–60fps)Recommended upload bitrate
Apple HLS, 1080p H.2646 and 7.8 MbpsTop rungs of Apple's example 30fps bitrate ladder
Netflix, Ultra HD15 Mbps or higherConnection speed Netflix recommends for 4K playback
ATSC 1.0 broadcast19.39 MbpsTotal payload of one 6 MHz channel, shared by every program on it
Cinema DCP (DCI)250 MbpsMaximum JPEG 2000 image bitrate

Sources: YouTube upload encoding settings, Apple HLS Authoring Specification, Netflix internet speed recommendations, ATSC A/53 and the DCI Digital Cinema System Specification.

Speed Ramping & Time Effects

A speed ramp changes playback speed within one shot. Its screen time is the sum of each segment's real-time length divided by the speed it plays at.

Screen Time of an Overcranked Shot
Screen Time = Real-Time Duration × (Capture FPS ÷ Playback FPS)

How long a high-frame-rate shot lasts when every frame is played at the timeline rate.

Where

Real-Time Duration
How long the action took on set(seconds)
Capture FPS
Camera frame rate(fps)
Playback FPS
Timeline frame rate(fps)

Example: 5 seconds of action shot at 240fps, played at 24fps

Calculation:
5 seconds × (240 ÷ 24) = 50 seconds
Result:
5 seconds becomes 50 seconds on screen (10% speed)
Multi-Segment Speed Ramp
Total Duration = Σ(Segment Duration ÷ Speed)

Speed is a fraction of real time: 1 for normal speed, 0.5 for half speed, 2 for double speed.

Example: Action sequence: 2s normal, 3s at 50% speed, 1s normal

Calculation:
(2÷1) + (3÷0.5) + (1÷1) = 2 + 6 + 1 = 9 seconds
Result:
9 seconds total duration

Data Rate Planning

Offloads and transfers run at the speed of the slowest link: the card reader, the cable, the network or the destination drive. For uploads, the free upload time calculator gives the time at your connection speed in your browser.

Data Transfer Time
Transfer Time (s) = File Size (GB) × 8 ÷ (Link Speed (Gbps) × Efficiency)

Multiply by 8 to turn gigabytes into gigabits. Efficiency covers protocol overhead: about 0.8 is a fair planning figure for networks.

Where

File Size
Size of the data to move(GB)
Link Speed
Rated speed of the connection(Gbps)
Efficiency
Share of the rated speed you actually get(0 to 1)

Example: 100 GB over 10 Gigabit Ethernet

Calculation:
100 × 8 ÷ (10 × 0.8) = 100 seconds
Result:
About 1 minute 40 seconds, if both drives keep up. A single SATA SSD at about 550 MB/s needs 3 minutes for 100 GB, so it becomes the bottleneck.

Connection Speeds

ConnectionRated SpeedTypical Real-WorldBest Use Case
USB 3.0 (USB 3.2 Gen 1)5 Gbps~3.5 Gbps (8b/10b encoding caps it at 4)Card readers, backup drives
Thunderbolt 340 Gbps~22 Gbps (PCIe data)RAIDs and fast external SSDs
10 Gigabit Ethernet10 Gbps~8 GbpsShared storage, collaboration
SATA SSD6 Gbps~4.4 Gbps (about 550 MB/s)Local editing, cache drives

Practical Applications

Two worked examples that combine the formulas above.

Case study

Multi-Camera Documentary Workflow

  • Documentary Series
  • Advanced
  • 10 days

Scenario

A documentary crew films interviews with four cameras, 8 hours a day for 10 days: one UHD A camera and three HD cameras.

Challenge

Calculate total storage, including backups, before the shoot.

Solution

  1. Calculate per-camera storage from each codec's data rate
  2. Multiply by hours per day and shooting days
  3. Multiply by the number of backup copies
  4. Plan a daily offload and checksum verification

The numbers

  • Camera A (UHD ProRes 422 HQ, 23.976 fps): 8 hrs × 707 Mbps = 2,545 GB/day
  • Cameras B, C and D (1080p ProRes 422, 23.976 fps): 3 × 8 hrs × 117 Mbps = 1,264 GB/day
  • Total daily footage: 2,545 + 1,264 = 3,809 GB/day
  • 10 days total: 3,809 × 10 = 38,090 GB ≈ 38 TB
  • Three copies (3-2-1): 38 TB × 3 = 114 TB total storage needed

Result

The shoot needs about 114 TB across all copies, and nearly 4 TB of offload and verification every day.

Key takeaways

  • Storage grows in direct proportion to cameras, hours and bitrate
  • Daily offload is critical: don't let footage pile up on cards
  • One UHD camera can outweigh three HD cameras
  • A backup you have not verified is not a backup

Case study

International Delivery Planning

  • Feature Film Distribution
  • Advanced
  • Worked example

Scenario

A distributor needs a 120-minute feature delivered in 15 versions for different territories and platforms.

Challenge

Estimate storage, render time and QC time for all the versions.

Solution

  1. Keep one master: 4K DCI (4096 × 2160) ProRes 4444 at 24fps
  2. Render each deliverable from the master
  3. QC the master in full, then spot-check each deliverable
  4. Run renders in parallel where the hardware allows

The numbers

  • Master: 120 min × 1,131 Mbps = 1,018 GB
  • 15 deliverables averaging 50 Mbps: 45 GB each, 675 GB in total
  • Total storage: 1,018 + 675 + 500 GB of working files ≈ 2.2 TB
  • Render time: 15 versions × 3 hours = 45 machine-hours
  • QC: one real-time pass of the master (2 hours) plus 15 minutes of spot checks per version (3.75 hours)

Result

About 2.2 TB of storage, 45 machine-hours of rendering and 6 hours of QC. Rendering on three machines in parallel brings the renders to about 15 hours.

Key takeaways

  • Every deliverable inherits the quality of the master
  • Parallel rendering shortens the schedule but not the machine-hours
  • QC the master in full in real time; spot-check the versions made from it

Calculators for this guide