Residence Time Calculator (Hold-Up Time, τ = V ÷ Q)
By Santaji GadepatilinUpdated November 5, 2026
Residence time is the average time a fluid spends inside a vessel — the liquid volume divided by the throughput. This residence time calculator works out τ = V ÷ Q for tanks, reactors, settling basins and pipes, and the space velocity (tank turnovers per hour).
How to use the residence time calculator
Enter the working (liquid) volume and the flow rate through the vessel. The calculator returns the residence time and the space velocity. To size a vessel, clear the volume and enter the residence time you need.
Residence time formula
τ = V ÷ Q · SV = 1 ÷ τ
Worked example
A 10 m³ buffer tank with 5 m³/h flowing through it:
- τ = 10 ÷ 5 = 2 h (120 min)
- Space velocity = 1 ÷ 2 h = 0.5 h⁻¹
Residence time by volume and flow
| Volume | 2 m³/h | 5 m³/h | 10 m³/h | 20 m³/h | 50 m³/h |
|---|---|---|---|---|---|
| 1 m³ | 30 min | 12 min | 6 min | 3 min | 1 min |
| 5 m³ | 2.5 h | 60 min | 30 min | 15 min | 6 min |
| 10 m³ | 5.0 h | 2.0 h | 60 min | 30 min | 12 min |
| 25 m³ | 12.5 h | 5.0 h | 2.5 h | 75 min | 30 min |
| 50 m³ | 25.0 h | 10.0 h | 5.0 h | 2.5 h | 60 min |
| 100 m³ | 50.0 h | 20.0 h | 10.0 h | 5.0 h | 2.0 h |
Notes
- Use the liquid volume at normal operating level, not the vessel’s total volume — get it from the vertical tank or horizontal tank calculator.
- For a pipe, residence time = length ÷ velocity.
Frequently asked questions
What is the residence time formula?
τ = V ÷ Q — the working volume of the vessel divided by the volumetric flow rate through it. 10 m³ with 5 m³/h flowing through gives 2 hours.
Is residence time the same as space time?
For a reactor, space time τ = V ÷ Q₀ is based on the inlet flow. It equals the mean residence time when the fluid density does not change through the reactor.
What is space velocity?
The reciprocal of space time — how many vessel volumes pass through per hour. A residence time of 2 hours is a space velocity of 0.5 h⁻¹.
Do all particles stay for τ?
Only in ideal plug flow. In a well-mixed tank, residence times follow an exponential distribution — about 63% of the fluid leaves before τ.