Culvert Sizing Calculator
Manning's Equation describes how much flow a pipe can carry based on its size, roughness, and the slope it's laid on — the same equation used for open channels, rearranged here to solve directly for the diameter a circular culvert needs to carry a design flow while flowing full. Rather than iterating by hand across standard pipe sizes, this calculator solves for the exact theoretical diameter and then rounds up to the nearest standard nominal size actually available to order.
The Formula
D = (Q × n / (k × √S))³⁄⁸
Q is the design flow rate, n is Manning's roughness coefficient (0.013 is a common default for concrete pipe), S is the slope, and k is a constant that folds in the pipe's geometric shape factor and a unit-conversion constant (1.49 for imperial units, 1.0 for metric).
Required Diameter by Design Flow
| Design flow | Theoretical diameter | Standard size (rounded up) |
|---|---|---|
| 10 cfs | 17.7 in | 18 in |
| 25 cfs | 24.9 in | 30 in |
| 50 cfs | 32.3 in | 36 in |
| 100 cfs | 41.9 in | 42 in |
| 200 cfs | 54.3 in | 60 in |
Doubling the design flow from 100 to 200 cfs doesn't double the required diameter — because diameter scales with flow raised to the 3/8 power, it increases by a much smaller factor, roughly 30% in this example.
Where This Gets Used
- Sizing a culvert for a road crossing — converting a design storm's peak flow into a specific pipe size to order and install.
- Checking an existing culvert's adequacy — comparing an existing pipe's size against what a higher design flow (from updated rainfall data or upstream development) would now require.
- Early-stage drainage planning — a first-pass sizing before a full hydraulic analysis that also checks inlet and outlet control.
How to Use This Calculator
- Choose Unit system — Imperial (cfs, ft/ft) or Metric (m³/s, m/m).
- Enter Design Flow Rate and Slope.
- Optionally adjust Manning's n (defaults to 0.013 for concrete pipe).
- Select Calculate to see the theoretical required diameter and the recommended standard nominal size.
Related Calculations
Estimate the peak runoff feeding this culvert with the Drainage Flow Calculator, or check pavement design over the crossing with the Pavement Thickness Calculator.