Time of Concentration Calculator

Calculate the Time of Concentration (T_c) for a watershed using the Kirpich Formula. This metric is essential for hydrologic modeling and calculating peak discharge using the Rational Method.

Distance from most remote point to outlet.

Total drop divided by flow length (Decimal).

Estimated Time of Concentration (T_c)

0.00

Minutes

What is Time of Concentration?

In hydrology, the Time of Concentration (T_c) represents the time required for water to travel from the hydraulically most distant point in a watershed to the point of interest (usually the drainage outlet). Understanding T_c is critical for predicting how a watershed will respond to a rain event.

Understanding the Kirpich Formula

The Kirpich Equation is one of the most widely used empirical formulas for calculating flow time in small, agricultural, or urban watersheds. The formula is expressed as:

T_c = 0.0078 × L^0.77 × S^-0.385

• T_c: Time of concentration in minutes.
• L: Length of the flow path in feet.
• S: Average slope of the flow path (ft/ft).

Why is T_c Important?

1. Rational Method: T_c is directly used to determine the rainfall intensity (I) from Intensity-Duration-Frequency (IDF) curves.
2. Flood Risk: Shorter T_c values usually indicate faster runoff and higher peak flow rates, increasing flash flood potential.
3. Infrastucture Design: Civil engineers use this data to size culverts, storm drains, and detention ponds appropriately.

Step-by-Step Calculation Example

Assume you have a small drainage area with the following characteristics:

• Flow Length (L): 1,200 feet
• Elevation Drop: 24 feet
• Slope (S): 24 / 1,200 = 0.02 ft/ft (or 2%)

Applying the formula:

1. T_c = 0.0078 × (1200)^0.77 × (0.02)^-0.385

2. T_c = 0.0078 × 235.15 × 4.50

3. T_c ≈ 8.26 Minutes

function calculateTc() { var L = document.getElementById("flowLength").value; var S = document.getElementById("slope").value; var resultDiv = document.getElementById("tcValue"); var wrapperDiv = document.getElementById("tcResultWrapper"); if (L === "" || S === "" || parseFloat(L) <= 0 || parseFloat(S) <= 0) { alert("Please enter valid positive numbers for both Flow Length and Slope."); return; } var length = parseFloat(L); var slope = parseFloat(S); // Kirpich Formula: Tc = 0.0078 * (L^0.77) * (S^-0.385) // L is in feet, Tc is in minutes var tc = 0.0078 * Math.pow(length, 0.77) * Math.pow(slope, -0.385); if (isNaN(tc) || !isFinite(tc)) { alert("The calculation resulted in an error. Please check your slope input."); return; } resultDiv.innerText = tc.toFixed(2); wrapperDiv.style.display = "block"; }