Slow Motion Calculations

Updated

The math of overcranking: slow-motion factor and speed from the capture and timeline frame rates, running time, frame counts, speed ramps, and what a high frame rate does to shutter, light and NTSC timing.

Frame Rate Reference Guide

Common Frame Rates

24fps

Cinema Standard

The base rate for the slow-motion factors on this page

30fps

Standard Video

Web video, and TV in 60 Hz regions (as 29.97)

60fps

2.5x Slow Motion

Gentle slow motion at 40% speed on a 24fps timeline

120fps

5x Slow Motion

20% speed on a 24fps timeline

High-Speed Capture

240fps

10x Slow Motion

10% speed on a 24fps timeline

480fps

20x Slow Motion

5% speed on a 24fps timeline

960fps

40x Slow Motion

2.5% speed on a 24fps timeline

1000fps+

Specialist Cameras

Dedicated high-speed cameras such as the Phantom range

Playback Standards

23.976fps

24 × 1000/1001

24p in systems derived from NTSC

25fps

PAL Standard

Broadcast in 50 Hz regions

29.97fps

30 × 1000/1001

Broadcast in 60 Hz regions

50/59.94fps

Progressive HD

Sports and smooth-motion delivery

Slow Motion Calculations

Slow Motion Factor and Speed

How much slower footage plays when it is captured at one frame rate and played on a timeline at another.

Formula:

Slow Motion Factor = Capture FPS ÷ Playback FPS; Speed % = Playback FPS ÷ Capture FPS × 100

Examples:

120fps captured, 24fps playback

Calculation: 120 ÷ 24 = 5x slower

Result: 5x slow motion (20% speed)

240fps captured, 30fps playback

Calculation: 240 ÷ 30 = 8x slower

Result: 8x slow motion (12.5% speed)

Tips:

  • To get a given slowdown without interpolated frames, capture at playback rate × the slowdown
  • Work from the timeline rate you will deliver at: the same 120fps clip is 5x on 24fps and 4x on 30fps. The free speed change calculator does the math in your browser
  • High frame rates fill cards fast: see storage planning

Running Time

How long a slow-motion shot runs on the timeline, from how long it took in real time.

Formula:

Timeline Duration = Real-Time Duration × (Capture FPS ÷ Playback FPS)

Examples:

10 seconds at 120fps on a 24fps timeline

Calculation: 10 × (120 ÷ 24) = 50 seconds

Result: 50 seconds on the timeline

5 seconds at 240fps on a 30fps timeline

Calculation: 5 × (240 ÷ 30) = 40 seconds

Result: 40 seconds on the timeline

Tips:

  • Slow motion eats running time: a 5-second action at 240fps fills 40 seconds of a 30fps cut
  • Shoot only the moment you need, then ramp in and out of it

Frame Count

How many frames a high-speed take records.

Formula:

Total Frames = Real-Time Duration (seconds) × Capture FPS

Examples:

3 seconds at 240fps

Calculation: 3 × 240 = 720 frames

Result: 720 frames captured

8 seconds at 120fps

Calculation: 8 × 120 = 960 frames

Result: 960 frames captured

Tips:

  • Divide the frame count by the timeline rate for the running time: 720 frames at 24fps is 30 seconds
  • Cameras with a fixed high-speed buffer record a set number of frames, so check it against this count

Speed Ramping

Work out how long a linear speed ramp plays on the timeline. This holds when the speed changes evenly over the ramp's timeline duration (a straight line on the retime curve): the ramp then plays at its average speed. Eased or curved ramps need the area under the curve instead.

Formula:

Ramp Timeline Duration = Source Duration ÷ ((Start Speed + End Speed) ÷ 2)

Examples:

2 seconds of source, ramped from 100% to 25%

Calculation: 2 ÷ ((1.00 + 0.25) ÷ 2) = 2 ÷ 0.625 = 3.2 seconds

Result: 3.2 seconds on the timeline

1 second of source, ramped from 50% to 10%

Calculation: 1 ÷ ((0.50 + 0.10) ÷ 2) = 1 ÷ 0.30 = 3.33 seconds

Result: 3.33 seconds on the timeline

Tips:

  • The slowest clean speed is playback FPS ÷ capture FPS: 20% for 120fps material on a 24fps timeline
  • Below that speed the editor repeats or interpolates frames
  • Ease the ramp in and out, and time the slowest point to the action beat

Shutter and Light at High Frame Rates

Keeping the same shutter angle at a higher frame rate shortens every exposure, which costs light and changes the motion blur.

Formula:

Exposure Time = (Shutter Angle ÷ 360) ÷ FPS; Stops Lost = log2(New FPS ÷ Old FPS)

Examples:

180° shutter, 24fps to 120fps

Calculation: (180 ÷ 360) ÷ 120 = 1/240 s; log2(120 ÷ 24) = 2.32

Result: 1/240 s per frame, about 2⅓ stops less light

How the blur looks on a 24fps timeline

Calculation: 1/240 s at 24fps = 360 × 24 ÷ 240

Result: The motion blur of a 36° shutter at 24fps

Tips:

  • Slowed footage looks crisper than normal 24p because each frame carries less blur
  • Lights that flicker do so at twice the mains frequency (100 Hz or 120 Hz); exposures shorter than one cycle show it as pulsing
  • Test any LED, fluorescent or discharge light at the frame rate and shutter you plan to use; the shutter angle guide lists flicker-free settings

Fractional and Whole Frame Rates

Mixing a whole capture rate with a 1000/1001 timeline rate leaves a factor that is not quite round.

Formula:

Speed % = Timeline FPS ÷ Capture FPS × 100

Examples:

120fps on a 23.976fps timeline

Calculation: 23.976 ÷ 120 × 100 = 19.98%

Result: 5.005x: a 10-second take runs 50.05 seconds

119.88fps on a 23.976fps timeline

Calculation: 23.976 ÷ 119.88 × 100 = 20%

Result: Exactly 5x

Tips:

  • Pick the high-speed rate from the same family as the timeline: 119.88 for 23.976, 120 for 24 (the frame rates guide explains 23.976 vs 24)
  • A 0.1% speed difference is invisible in a short shot but drifts against sound over a long one