Dolly Track Curve Radius Calculator for Film Production

Curved dolly track is a set of rail sections bent to a specific radius, used to guide a camera dolly in an arc rather than a straight line. It is used whenever the shot calls for the camera to travel in a curved path: orbiting around a subject, sweeping from one angle to another through a curve, revealing something around a corner, or executing a circular pass that creates the cinematic sense of the camera wrapping around the story. The track is made from the same aluminum rail material as straight track and connects using the same tie plates and hardware, so any dolly designed for standard rail track can run on curved sections. In the US, standard curved track section length is 4 feet, bent to a specific radius and sold or rented as individual sections that join together to form the required arc.

An orbit shot is a specific type of curved dolly move where the track forms a circle centered on the subject, and the camera rotates around the subject at a fixed radius. The subject remains roughly centered in frame throughout the move while the background rotates 360 degrees or a portion thereof. A regular curved dolly move, sometimes called an arc or banana move, uses curved track to carry the camera in a curve from one position to another without necessarily keeping the subject centered. Both use the same curved track hardware and the same radius calculations, but the shot planning context is different. For an orbit shot, the track radius equals the desired camera-to-subject distance. For a curved arc, the radius is determined by the geometric relationship between the two camera positions and the available floor space.

Track radius is the radius of the imaginary circle of which your curved track section forms an arc. If you extended all of your curved track sections into a full circle, the radius of that circle would be your track radius. A smaller radius creates a tighter, more aggressive curve; a larger radius creates a more gentle, sweeping arc. For an orbit shot, track radius equals camera-to-subject distance, because the track arc is part of a circle centered on the subject. For a 10-foot-radius orbit, the camera is 10 feet from the subject throughout the move. For non-orbit arc shots, the radius describes the geometry of the curve without necessarily having a direct relationship to subject distance, depending on where the subject falls relative to the center of the track’s circle.

The chord-and-sagitta method lets you determine the required track radius from two tape measure readings at the location. The chord is the straight-line distance from where you want the camera to start the move to where you want it to end. The sagitta is the maximum distance the track can push perpendicularly away from that straight chord line, which is determined by the available floor space at the location. With these two measurements, the required radius is exactly R = (C squared divided by four plus h squared) divided by two times h, where C is the chord and h is the sagitta. This formula is algebraically exact and gives you the precise radius in the same measurement units as your inputs. Enter the chord and sagitta into Mode 2 of this calculator and it applies the Big.js precision calculation for you.

Sagitta is the depth of an arc, measured as the perpendicular distance from the midpoint of a chord to the midpoint of the arc. In practical grip terms, it is how far the curved track pushes into the room perpendicular to the straight line between the track’s start and end points. Sagitta is the critical measurement for space planning at a location because it tells you the maximum footprint of the arc perpendicular to the chord. If the sagitta is greater than the available space between the chord line and the nearest obstacle (a wall, a set piece, a lighting stand), the track will not fit. Sagitta grows rapidly with arc angle and more slowly with radius: a 90-degree arc at 10 feet has a sagitta of 2.93 feet, while the same radius at 180 degrees has a sagitta of 10 feet (equal to the radius itself). Always check the sagitta against available floor space before committing to an arc design.

Major US grip rental houses in production centers including Los Angeles, New York, Atlanta, and Chicago typically stock curved track sections in the following standard radii: 5 feet (tight, good for single-subject close quarters), 7.5 feet (medium, good for a single subject with some breathing room), 10 feet (the most widely rented radius in US narrative production), 12 feet, 15 feet, and 20 feet. Some larger houses also stock 25-foot and 30-foot sections for very gentle arcs and automotive work. Radii tighter than 5 feet (for example, 3-foot radius for very confined setups) are available at specialty houses or by custom order. If your calculated radius falls between standard sizes, discuss the options with your grip rental house: they may have the exact radius in stock from a previous custom order, or they may be able to bend custom sections for a feature-length show or commercial.

A 90-degree arc at 10-foot radius has an arc length of approximately 15.71 feet (10 times pi over two). At 4 feet per section, you need 4 sections (4 times 4 equals 16 feet, which is slightly more than 15.71 feet). As a practical rule, always round up to the next whole section, and then add 1 to 2 sections as a buffer for final position adjustment. So for a 90-degree orbit at 10 feet, order 5 to 6 sections and use 4 in the actual arc. The chord for this setup is 14.14 feet (2 times 10 times sine of 45 degrees) and the sagitta is 2.93 feet. This means the track pushes approximately 3 feet forward from the chord, which is a useful spatial planning number for positioning the arc in the space.

In the United States, Chapman/Leonard and Fisher dollies use compatible track rail profiles, and in most cases their curved track sections at the same radius are interchangeable. This interchangeability is one of the practical advantages of the US production track system: if one house is short on 10-foot-radius sections, you can supplement from another house’s inventory. However, always physically verify interchangeability before the shooting day, as minor manufacturing variations between production runs can occasionally create a slight misalignment at the joint. Elemack and Panther track (European systems) use a different rail profile and are not compatible with Chapman/Leonard or Fisher sections. If your production uses a European dolly system, confirm track compatibility with your specific rental house.

For the Chapman Leonard Hybrid and Fisher 10 dollies, the minimum safe track radius for smooth operation without binding or instability is generally considered to be 5 feet. At radii tighter than 5 feet, the dolly’s wheels can bind on the rail at the inner curve, creating a jerky, uneven movement that registers on camera. The Chapman PeeWee dolly, which has a narrower wheelbase and was specifically designed for tight spaces, can operate on 3-foot radius track. The correct minimum radius for any specific dolly model should be confirmed with the manufacturer or rental house, as different wheel configurations and bearing types affect the minimum usable radius. Operating any dolly below its minimum rated curve radius is a safety concern and can damage both the dolly and the track.

Track radius has a significant effect on the visual quality and feel of a dolly arc shot. A tighter radius (5 to 7.5 feet) creates an arc where the background shifts and rotates dramatically even for a modest dolly movement, producing a dynamic, energetic feel that emphasizes the subject’s isolation or power. A wider radius (15 to 20 feet) at the same linear dolly speed creates a more subtle, graceful arc where the background shifts slowly, producing a cinematic, contemplative quality. The relationship between lens focal length and track radius also matters: a tighter radius with a longer lens can produce a subtle, compressed swirl effect that feels very cinematic, while a tighter radius with a wide angle lens can feel unnatural and disorienting. Most narrative DPs work with track radii between 8 and 15 feet at focal lengths between 35mm and 85mm equivalent for the most natural-feeling arc.

A compound curve is a track path that uses two or more different radii in the same run, creating an S-curve or other non-circular arc. In film production, compound curves are used when the camera needs to follow a subject through a turning corridor, transition from one angle to another through a complex path, or thread through a set that has obstacles at different points. Unlike a simple arc, a compound curve requires mixing curved sections of different radii in the same track run. The transitions between sections of different radii must be smoothed by the dolly grip during the move, often using skilled counterweighting or manual assistance on the dolly to prevent jerk at the radius change. Compound curves are significantly more complex to plan and execute than simple arcs and require an experienced dolly grip and extra prep time. This calculator handles only single-radius arcs.

There are two reliable methods for marking curved track position on a location floor during prep. The first method uses the chord and sagitta. Establish the chord line with tape (marking the start and end of the track arc) and then mark the midpoint of the chord. Measure the sagitta distance perpendicular to the chord midpoint and mark the apex of the arc. A third person can hold one end of a tape measure at the center of the circle (which is the sagitta distance beyond the apex point) while the grip runs the other end along the floor at the calculated radius distance, drawing the arc with a china marker or chalk. The second method, useful when the center of the circle is accessible, is to physically locate the center point at radius R from the track apex and swing an arc using the tape measure. Both methods should result in the same arc. Confirm by checking that the chord endpoints are both exactly the chord length apart and exactly the radius distance from the calculated center.

A round-table or 360-degree orbit shot has the camera complete a full circle around the subject, requiring enough curved track sections to form a complete circle at the specified radius. The number of 4-foot sections needed is the circumference divided by the section length: 2 times pi times R, divided by 4. For a 10-foot radius full orbit, you need approximately 16 sections totaling 62.8 feet of track. The track connects end to end in a circle, with the dolly running continuously around the full circle in one take or multiple complete orbits. The main challenge is lighting: a 360-degree orbit will at some point show all four walls of the room, making it nearly impossible to hide lights in the conventional way. Most 360 orbits use ceiling-mounted lighting rigs or naturalistic practical lighting to avoid visible light sources as the camera sweeps the room. The dolly cable routing also requires careful planning to prevent the cable from appearing in frame or becoming tangled on a full orbit.

Lens focal length does not change the track radius or arc length needed for a geometric arc. The required arc length is purely a function of the orbit radius and arc angle. However, focal length significantly affects how the arc looks on camera and therefore what angle of arc feels sufficient for a given creative purpose. A longer focal length compresses background movement relative to subject movement, meaning that a 90-degree arc on a 10-foot radius at 85mm looks very different from the same arc at 24mm. At longer focal lengths, the background rotation appears less dramatic for the same arc angle, so DPs sometimes specify a larger arc angle at longer focal lengths to achieve the same visual effect. The practical implication is that the DP should specify both the track radius and the arc angle, not just one or the other, and the grip team should calculate and verify the arc length and sagitta for the specific combination specified.

Before any dolly runs on curved track, the key grip should verify several safety points. First, confirm that all section joints are fully seated and tied with tie plates: a section that separates during a dolly move can cause the dolly to derail, potentially injuring crew near the track. Second, check that the dolly’s inner and outer wheels are correctly positioned on the rails for the radius in use: at tighter radii, the wheel geometry changes and the dolly should be checked for smooth, wobble-free movement through the full arc before any takes with camera and operator aboard. Third, verify the cable routing for the dolly’s power and data cables so that they do not create a trip hazard or appear in the shot at any point in the arc. Fourth, confirm that all lighting equipment and sandbags are clear of the dolly’s path through the full arc, not just at the start and end positions. Walk the full arc on foot at the pace of the planned dolly move before the camera is mounted.

This calculator is specifically designed for dolly track arcs, where the physical track rail forms the curved path. For crane arm swings and remote head rotations, the geometry is different: the arm pivots around a fixed point, and the camera’s arc radius equals the arm length at the camera end. The formulas for arc length and chord are mathematically identical (arc = R x theta, chord = 2R x sin(theta/2)), but the planning context is different. For a crane arm swing, the radius is fixed by the arm length, and the key planning challenge is boom height and the travel arc at the lens position. You can use this calculator’s Mode 1 to calculate arc length, chord, and sagitta for any crane arm swing by treating the arm length as the radius and the intended sweep angle as the arc angle. The results will give you the physical dimensions of the camera’s travel path, which is useful for confirming clearance around obstacles during pre-production planning.