---
title: "How to Measure a Curved Cushion: Chord, Rise and Radius"
url: "https://cushionguide.com/guides/curved-cushion-chord-rise-radius/"
section: "The Pattern Room"
author: "Nate Kowalski, The Pattern Engineer of Detroit"
author_url: "https://cushionguide.com/masters/nate/"
published: "2026-04-02"
updated: "2026-09-24"
keywords: "how to measure a curved cushion, curved bench cushion, rounded end cushion, curved banquette cushion, cushion radius formula"
---

# How to measure a curved cushion with a chord, a rise and one formula

*Curves scare people. They shouldn't. A curve is two straight measurements and a little arithmetic, and when it isn't, it's a sheet of paper and a marker. Here's the whole method, with a 245-inch fire-pit bench as proof.*

> **The quick answer:** To measure a curved cushion, stretch a straight line from one end of the curve to the other (the chord), then measure from the middle of that line out to the curve (the rise). The radius is r = (c²/4 + h²) / 2h. For long or uneven curves, add offsets every 4 in (10 cm); for anything stubborn, trace a full-size paper template.

![Caramel bouclé cushion on a built-in plaster bench in an arched niche with rust, patchwork and black pillows under a lantern](https://cushionguide.com/media/bench-cushions/caramel-boucle-cushion-arched-niche-bench-1600.webp "A caramel cushion made to fit a built-in plaster bench under an arch, with an iron lantern and an olive tree.")

## One number can't describe a curve

A curved edge given as a single number can't be cut. A buyer once wrote to the workshop with a curved edge of 17 in (43 cm), and the workshop replied with one question: how far does the curve sit from the middle of that straight line?

That distance has a name. Draftsmen call it the sagitta; I call it the rise. Pair it with the straight line across the curve, the chord, and you can rebuild the arc on any cutting table. Angles are just lengths in disguise, and so are curves.

Almost nobody teaches this, partner, so here is how to measure a curved cushion, one move at a time. First, what are you measuring: a rounded corner, a curved bench, or a banquette that bends around a table?

## Eight moves from curve to cutting diagram

1. **Mark where the curve starts and stops**: Put a strip of tape at each end of the curve and measure every straight edge up to those marks. For a rounded corner, give both edges as if the corner were square, then note how far from the corner the curve begins on each edge, say 8 in (20 cm) each way.
2. **Stretch the chord**: Pull a string or lay a straightedge from one tape mark to the other. The straight distance between them is the chord, c. Measure it to the nearest 1/8 in.
3. **Measure the rise at the middle**: Find the midpoint of the chord. From there, measure square to the line, at 90°, out to the curve. That is the rise, h. A small rise hides easily, so take it twice.
4. **Work the radius**: The cushion radius formula is r = (c²/4 + h²) / 2h. Say the chord is 48 in and the rise is 6 in: (576 + 36) / 12 = 51 in (130 cm). It holds for a shallow bow and for an arc past a half circle alike. A phone calculator does the rest.
5. **Take offsets every 4 in on long curves**: Mark the chord every 4 in (10 cm) and measure from the line out to the curve at each mark. On a true arc the offsets rise and fall evenly on both sides of the middle. If they don't, it isn't a circle, and the list of offsets becomes the shape.
6. **Measure both edges of a curved bench**: A bench curves twice. Lay a string along the inner curve and along the outer curve, then measure each string flat, or use a flexible tape. Add the straight end-to-end distance of each edge and the depth at both ends and in the middle.
7. **Trace a template when the curve won't behave**: Lay wrapping paper or newspaper on the seat, trace the edge with a marker, cut it out, and photograph it flat beside a tape measure. Mark where each curve begins. Keep the paper and send the photos.
8. **Approve the redraw before cutting**: The workshop redraws your curve as its own diagram and sends it back for approval. Check it top side up, as seen standing in the room, and approve it before anything is cut.

> **Tailor's margin:** Give a curve as chord plus rise, never as one length. A 17 in (43 cm) curved edge tells the cutter nothing about how far it bows.

## A 245-inch fire-pit bench, measured with a string

A buyer in the US wanted cushions for a curved stone bench around an outdoor fire pit and measured it with a string. Good instinct. The workshop asked for more: the inner curve, the outer curve, the depth at several points, and the straight end-to-end distance along the back and along the front.

Those chords came back as 142 in (361 cm) at the back and 117 in (297 cm) at the front. From them the workshop drew the curved bench cushion: a 245 in (622 cm) outer curve, a 208 in (528 cm) inner curve, 12 3/4 in (32 cm) deep and 3 in (7.5 cm) thick.

At about 20 ft (6 m) of seat, one cushion would have been a wrestling match. It was split into 4 symmetrical segments for handling and storage, in an outdoor fabric in a heather beige tone. Two arc lengths plus two chords: that is what let the curve be rebuilt exactly.

## Which method for which curve

| Curve | Send this | Worth knowing |
|---|---|---|
| Rounded corner | Both edges as if square, plus where the curve starts on each | Note each corner separately if they differ |
| One shallow arc: arched window seat, bench end | Chord, rise and the straight runs on either side | Drawn as a rectangle plus an arc of a circle |
| Long curved bench: fire pit, pew, round sofa | Inner and outer curves, both chords, depth at the ends and the middle | Made as matching segments that join |
| Uneven, S-shaped or kidney curve | Full-size paper template, photographed flat beside a tape | Reviewed first; may be declined |

## Curves that travel well, and the ones that get a polite no

Mild curves are routine. Strong ones are reviewed by the craftsmen before anyone promises anything, because a curve that is slightly wrong is wrong along its whole length.

Honest refusals from past orders: a round bay window whose curve was too pronounced, a rocking-chair seat pad that had to fit a shaped chair exactly, and covers-only re-covering of curved outdoor loveseat cushions. None could be made accurately from measurements without the piece in the workshop. Kidney or banana curves may be declined too, with a local upholsterer suggested instead.

Templates change the answer. An S-shaped (ogee) bench edge was first declined, then accepted once the buyer supplied a full template. Budget for it: a curved piece costs more than a plain trapezoid of the same size, and one curved order was quoted at about 10 to 12 business days of making. For a 33 x 20 in (84 x 51 cm) rounded end cushion, a buyer in the US sent the bench maker's drawing of the curve, and that drawing is what made it quotable.

## One long curve, or segments?

Long curves are made as matching segments that join cleanly and are easier to handle and wash. The fire-pit bench became four. For where the joins should go, see [one piece or two](https://cushionguide.com/guides/long-bench-cushion-one-piece-or-two/).

Some families still want one continuous curved banquette cushion. A family in the US with a curved kitchen banquette about 19 in (48 cm) deep asked for exactly that, with a toddler at the table, and had already made a full-size paper template. The workshop asked for photos of it with measurements marked, especially where each curve begins, and confirmed 3 in (7.5 cm) of 32-density foam (about 2 lb/ft³) with a fiber wrap, under covers that machine-wash at 86°F (30°C).

A full-size template is the most accurate curve measurement there is; the [paper template guide](https://cushionguide.com/guides/paper-template-for-custom-cushion/) shows how to make one that photographs well. Fire-pit rings have their own page in [fire-pit bench cushions](https://cushionguide.com/concepts/fire-pit-bench-cushions/), rounded corners in [the rounded-corner guide](https://cushionguide.com/guides/rounded-corner-cushion-measuring/), and the seats themselves in the [bench cushions](https://cushionguide.com/cushions/bench-cushions/), [banquette cushions](https://cushionguide.com/cushions/banquette-cushions/) and [patio and porch cushions](https://cushionguide.com/cushions/patio-and-porch-cushions/) hubs.

Chord, rise, offsets. Then paper.

## Curve mistakes the workshop keeps seeing

- ✗ A subtle curve described with numbers only. Without a drawing it reads as square.
- ✗ One arc length and no chord. An arc length alone can't tell a shallow bow from a deep one.
- ✗ A style photo instead of a sketch. The photo shows a look, not your seat.
- ✗ A curved cushion ordered through the rectangle listing. That route never asks for a drawing, so the shape can't be checked.
- ✗ One depth for a curved bench. Measure both ends and the middle.
- ✗ Mailing the paper template. Photograph it flat beside a tape measure instead.

> A curved cushion needs two straight numbers: the chord across the curve and the rise at its midpoint. The radius falls out of those.
>
> — Nate

## Buyer questions: curves, rounds and templates

**A common question:** How do I measure a bench with a rounded end, or a cushion that curves?

**The workshop's answer:** Give total width and depth, the straight length of each edge before the curve starts, where each curve starts and ends, and the curve's depth or radius, sketched on paper and photographed. For tricky curves, trace the seat onto paper, cut it out and photograph it flat beside a tape measure. Each cushion gets its own drawing.

**A common question:** How should I measure a curved fire-pit bench or a church pew?

**The workshop's answer:** Measure the inner curve along the front and the outer curve along the back with a flexible tape, or a string measured flat. Add the straight end-to-end distance, the depth at both ends and in the middle, and the thickness; 2 to 3 in (5 to 8 cm) is recommended. Very long curves are made as matching segments.

**A common question:** Is there any curve you won't make?

**The workshop's answer:** Mild curves are fine, but nothing curved is promised until the craftsmen review a measured drawing and photos. A too-pronounced round bay, an exact-fit rocking-chair seat and some curved covers-only jobs have been declined. An S-curve bench edge was declined, then made once the buyer supplied a full template.

**A common question:** Do I have to make a paper template and mail it to you?

**The workshop's answer:** No. A drawing with every edge measured is usually enough. A full-size template is the best start for a curve, though: photograph it with measurements marked, especially where the curves begin, and send the photos rather than the paper. The workshop redraws it as its own diagram for you to confirm.

**A common question:** My cushion has rounded corners. How do I write the size?

**The workshop's answer:** Write each edge's full length as if the corners were square, then mark how far from each corner the curve begins along both edges, for example 8 in on each side. Note each corner separately if they differ, or trace the corner on paper and photograph it beside a tape measure.

## Curve questions, answered short

### What is the rise, or sagitta, of a curve?

It is the distance from the midpoint of the chord, the straight line joining the two ends of a curve, out to the curve itself, measured at 90° to the chord. Together with the chord, it fixes the radius of a circular arc.

### Does the radius formula work on a curve deeper than a half circle?

Yes. r = (c²/4 + h²) / 2h holds for any circular arc; on a deep curve the rise simply comes out larger than the radius. If offsets taken every 4 in (10 cm) don't rise and fall evenly, the curve isn't circular and needs a template.

### How thick should a curved bench cushion be?

For curved benches the workshop recommends 2 to 3 in (5 to 8 cm). The standard seat cushion is 4 in (10 cm), and 3 to 4 in is the usual advice for outdoor benches. The 245 in fire-pit bench was made 3 in (7.5 cm) thick.

### Does a curved cushion take longer to make than a rectangle?

Usually. Curved and complex shapes go to the most experienced craftsman, and one curved order was quoted at about 10 to 12 business days of making; a curved piece also costs more than a plain trapezoid of the same size. Rectangular pieces in the same project are quoted normally.

## Related at the atelier

- [Custom Bench Cushion for a Curved Garden Bench in Slate Gray](https://cushionguide.com/readings/slate-gray-curved-garden-bench-cushion-roses/): A custom bench cushion for a curved-back garden bench should be cut to the inside of the frame, measured between the arms at seat level at both the front and the back.
- [Custom Garden Bench Cushion: Rainbow Herringbone on Silver Teak](https://cushionguide.com/readings/rainbow-herringbone-stripe-teak-garden-bench-cushion/): A multi-color stripe works on a garden bench when everything around it stays plain or textured: here an orange, teal and purple herringbone runs lengthwise on a custom box cushion, against silvered…
- [Custom Bench Cushion for a Narrow Café Bench in Aqua Microcheck](https://cushionguide.com/readings/aqua-microcheck-oak-cafe-bench-pad-marble-tables/): To make a narrow bench feel generous, cover its whole length with one continuous custom bench cushion in a fine, pale pattern.
- [How do I measure a curved bench, like a church pew or fire pit bench, for a cushion?](https://cushionguide.com/answers/curved-bench-cushion-measure-pew-fire-pit/): To measure a curved bench cushion, take the inner curve along the front edge and the outer curve along the back with a flexible tape or string, then the straight end-to-end distance and the depth at…
- [Standard cushion sizes, and when yours isn't one of them](https://cushionguide.com/guides/standard-cushion-sizes-chart/): Standard cushion sizes are store conventions rather than rules: US chair pads run about 15 to 18 in square, twin daybed mattresses 38 x 75 in (97 x 191 cm), chaise cushions about 72 to 75 x 22 to 24…
- [How do I measure a curved cushion or a bench with a rounded end?](https://cushionguide.com/answers/measure-curved-cushion-rounded-end/): To measure a curved cushion, sketch the seat with its total width and depth, the straight length of each edge before the curve starts, where each curve begins and ends, and the curve's depth or…
- [Getting a custom cushion quote: what to send so it's right the first time](https://cushionguide.com/guides/custom-cushion-quote-what-to-send/)
- [Commercial seating cushions for cafés, rentals and offices: what to specify](https://cushionguide.com/guides/commercial-cushions-cafe-rental-specs/)

*± 1/4 in — Nate*

---

Written by Nate Kowalski (https://cushionguide.com/masters/nate/) for CushionGuide (https://cushionguide.com/about/). The site explains made-to-measure cushions and the partner workshop makes them; measurements are in inches first. This Markdown mirrors the page at https://cushionguide.com/guides/curved-cushion-chord-rise-radius/