Overflow Flow Rate Calculator

Overflow/Weir Width (Inches)

Water Height Above Weir (Inches)

Estimated Flow Capacity:

0 GPH

0 Gallons Per Minute (GPM)

0 Cubic Feet Per Second (CFS)

How to Calculate Overflow Flow Rate

Calculating the flow rate over an overflow or weir is critical for aquarium hobbyists, pond builders, and civil engineers. This calculator uses the Francis Formula for a sharp-crested rectangular weir to estimate how much water can pass over a specific surface area based on the "head" (the height of the water above the edge).

The Formula

The standard simplified formula for a suppressed weir (where the weir width equals the channel width) is:

Q = 3.33 × L × H^1.5

Q: Flow rate in Cubic Feet per Second (CFS).
L: Length or width of the overflow (in feet).
H: Head height, or the depth of the water above the weir crest (in feet).

Key Factors to Consider

When designing an overflow system for a reef tank or a pool, remember these three factors:

Surface Tension: In very small overflows (short head height), surface tension can slightly restrict flow.
Drain Capacity: Your overflow box might handle 2,000 GPH, but if your drain pipe is too small, you will experience a flood. Ensure your plumbing matches your overflow capacity.
Safety Margin: Always design your overflow to handle at least 1.5x to 2x the flow of your return pump to account for blockages or algae growth.

Practical Example

If you have an aquarium overflow that is 12 inches wide and you want the water level to stay 0.5 inches above the teeth of the overflow:

Width (L): 12 inches = 1 foot.
Head (H): 0.5 inches = 0.0417 feet.
Calculation: 3.33 × 1 × (0.0417)^1.5 ≈ 0.0283 CFS.
Conversion: 0.0283 CFS × 448.83 ≈ 12.7 GPM, which is roughly 762 GPH.

function calculateOverflowRate() { var weirWidthInches = document.getElementById("weirWidth").value; var headHeightInches = document.getElementById("headHeight").value; var L = parseFloat(weirWidthInches); var H = parseFloat(headHeightInches); if (isNaN(L) || isNaN(H) || L <= 0 || H <= 0) { alert("Please enter valid positive numbers for both Width and Head Height."); return; } // Convert inputs to feet for the Francis Formula var L_feet = L / 12; var H_feet = H / 12; // Formula: Q (CFS) = 3.33 * L * H^1.5 var flowCFS = 3.33 * L_feet * Math.pow(H_feet, 1.5); // Convert CFS to GPM (1 CFS = 448.831 GPM) var flowGPM = flowCFS * 448.831; // Convert GPM to GPH var flowGPH = flowGPM * 60; // Display results document.getElementById("flowCFS").innerText = flowCFS.toFixed(4); document.getElementById("flowGPM").innerText = flowGPM.toFixed(2); document.getElementById("flowGPH").innerText = Math.round(flowGPH).toLocaleString(); document.getElementById("resultArea").style.display = "block"; }