Inputs
Circular arch segment geometryAll inputs and outputs use this unit.
Choose known values to compute the rest.
m
For inner and outer diameters.
m
Horizontal chord across the arch.
m
Vertical height from chord to arc at midspan.
m
If known, compute span, angle, and diameter.
m
With span, rise is determined.
Results
D = 2r
r = D/2
Sagitta
Chord length
θ = 2·asin(L/2r)
s = r·θ (radians)
If thickness provided
If thickness provided
Saved calculations
| # | Units | Mode | Span (L) | Rise (h) | Radius (r) | Diameter (D) | Angle (°) | Arc length (s) | Thickness | Di | Do |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | m | Span+Rise | 2.400 | 0.600 | 1.500 | 3.000 | 92.962 | 2.432 | 0.100 | 2.800 | 3.200 |
| 2 | m | Radius | 3.000 | 0.250 | 2.000 | 4.000 | 87.143 | 3.045 | 0.150 | 3.700 | 4.300 |
Click a row to load its values into the form.
Formulas used
For a circular arch segment with span L, rise (sagitta) h, and radius r:
- Radius from span and rise:
r = h/2 + L²/(8h) - Diameter:
D = 2r = h + L²/(4h) - Rise from span and diameter:
h = r - √(r² - (L/2)²), withr = D/2 - Span from radius and angle:
L = 2r·sin(θ/2) - Central angle (radians):
θ = 2·asin(L/(2r))→ degrees:θ° = θ·180/π - Arc length:
s = r·θ(θ in radians) - Inner/Outer diameters (optional):
Di = D − 2t,Do = D + 2twheretis thickness
How to use this calculator
- Select Units and the preferred Solve using mode.
- Enter the known values. For span+rise, both must be positive.
- Optionally enter Arch thickness to get inner and outer diameters.
- Click Calculate to populate the results area.
- Use Add to table to append results below for exporting.
- Use Export CSV or Download PDF for records.
- Click an example row to load its values back into the form.
Tip: A semicircle has D ≈ L when rise is half the span.
Quick reference: span L = 2.000 m — rise to diameter
Static examples for rapid checks. Scale linearly with chosen unit.
| Rise h (m) | Radius r (m) | Diameter D (m) | Angle θ (°) | Arc length s (m) |
|---|---|---|---|---|
| 0.250 | 2.125 | 4.250 | 56.145 | 2.082 |
| 0.500 | 1.250 | 2.500 | 106.260 | 2.318 |
| 0.750 | 1.042 | 2.083 | 147.480 | 2.681 |
| 1.000 | 1.000 | 2.000 | 180.000 | 3.142 |
Chord–angle table at r = 1.000 m
Use L = 2r·sin(θ/2), s = r·θ. Multiply values by your radius.
| Angle θ (°) | Chord L (m) | Arc length s (m) |
|---|---|---|
| 30 | 0.518 | 0.524 |
| 60 | 1.000 | 1.047 |
| 90 | 1.414 | 1.571 |
| 120 | 1.732 | 2.094 |
| 150 | 1.932 | 2.618 |
Thickness impact example (D = 3.000 m, θ = 120°)
Inner/outer diameters and arc lengths for selected thicknesses.
| Thickness t (m) | Di (m) | Do (m) | si (m) | so (m) |
|---|---|---|---|---|
| 0.000 | 3.000 | 3.000 | 3.142 | 3.142 |
| 0.050 | 2.900 | 3.100 | 3.037 | 3.246 |
| 0.100 | 2.800 | 3.200 | 2.932 | 3.351 |
| 0.150 | 2.700 | 3.300 | 2.827 | 3.456 |