Hydronic systems—whether serving fan coils, VAV reheat coils, radiant loops, or air handlers—are all governed by one simple relationship between flow rate, temperature change, and heat transfer. If you know the gallons per minute (GPM) flowing through a coil or piping loop, you can calculate how many BTUs per hour that flow can deliver. Likewise, if you know the heating or cooling load of a space, you can calculate the GPM required to meet that load.
This makes the GPM↔BTU/hr formula one of the most useful tools for HVAC designers, estimators, technicians, and project managers.
The Core Formula
The foundation of all hydronic heat-transfer calculations is:
BTU/hr = 500 × GPM × ΔT
Where:
- BTU/hr = heat transfer rate
- GPM = gallons per minute
- ΔT = temperature difference of the fluid (°F)
- 500 = constant (8.33 lb/gal × 60 min/hr × 1 BTU/lb-°F)
The constant will change slightly for glycol systems, but for pure water this is the standard value used throughout the HVAC industry.
Part 1 — Converting GPM to BTU/hr
When you know the flow rate and temperature difference, calculating the BTU/hr is straightforward.
Example 1: Heating Coil Output
A reheat coil receives:
- 4 GPM of hot water
- Entering water temperature: 180°F
- Leaving water temperature: 160°F
- Therefore, ΔT = 20°F
BTU/hr = 500 × 4 × 20
BTU/hr = 40,000
This coil delivers 40,000 BTU/hr of heating.
Example 2: Cooling Coil Load
A chilled water coil has:
- 55°F entering water temp
- 45°F leaving water temp
- ΔT = 10°F
- Flow = 18 GPM
BTU/hr = 500 × 18 × 10
BTU/hr = 90,000
This coil can reject 90,000 BTU/hr of heat (7.5 tons).
Part 2 — Converting BTU/hr to GPM
This is just the same formula rearranged:
GPM = BTU/hr ÷ (500 × ΔT)
This calculation is commonly used when:
- The heating or cooling load for a space is known.
- You’re selecting pump sizes.
- You’re sizing piping.
- You’re checking a coil schedule against thermal requirements.
- You’re validating reheat sizing for VAV systems.
Example 3: Required GPM for a Space Heating Load
A small office zone requires 32,000 BTU/hr of heating at design conditions. The system uses a 20°F temperature drop.
GPM = 32,000 ÷ (500 × 20)
GPM = 32,000 ÷ 10,000
GPM = 3.2 GPM
You need 3.2 GPM of hot water flow to meet the space heating demand.
Example 4: Required Chilled Water GPM
A conference room requires 75,000 BTU/hr of cooling.
The chilled water ΔT is designed for 12°F.
GPM = 75,000 ÷ (500 × 12)
GPM = 75,000 ÷ 6,000
GPM = 12.5 GPM
This space needs 12.5 GPM of chilled water to satisfy its cooling requirement.
Understanding the 500 Constant
Many students and young engineers wonder why the constant is 500. Before we move on, let’s take a deeper look at how this formula is built and what each part represents — especially the “1” inside the constant.
When we say the formula is:
BTU/hr = 500 × GPM × ΔT,
that 500 actually comes from three values multiplied together:
- 8.33 — the density of water in pounds per gallon
- 1 — the specific heat of water
- 60 — minutes per hour
8.33 × 1 × 60 ≈ 500
Now, that “1” in the middle is important.
It represents the specific heat of water — which is the amount of energy required to raise 1 pound of water by 1°F.
And for pure water, that value is essentially 1.0 BTU per pound per degree Fahrenheit.
But here’s the part many people miss:
The specific heat of water can change depending on what’s mixed with it.
Variances in Specific Heat for Real-World Systems
So in most commercial hydronic systems that use pure water, we can confidently use the constant 500.
But when you add glycol — which is common for freeze protection — the specific heat drops.
Glycol cannot carry as much heat per pound as water can.
For example:
- 20% glycol → specific heat drops to about 0.98
- 30% glycol → drops to around 0.94
- 40% glycol → drops further to about 0.90
When the specific heat decreases, the entire constant in the formula decreases.
That’s why, instead of using 500, we may use values like:
- 485 for light glycol mixtures
- 470 for medium concentrations
- 450 for heavy glycol mixtures
This means that glycol loops need more GPM to move the same number of BTUs, because the fluid carries less heat per pound.
- Water weighs 8.33 lb/gal
- It takes 1 BTU to raise 1 lb of water by 1°F
- There are 60 minutes in an hour
- Multiply: 8.33 × 60 ≈ 500
This is why the formula is universal across hydronic systems.
For glycol mixtures, the constant is reduced based on specific gravity and specific heat.
Useful Quick Reference Table
| ΔT (°F) | Approx. BTU/hr per 1 GPM |
|---|---|
| 10°F | 5,000 BTU/hr |
| 15°F | 7,500 BTU/hr |
| 20°F | 10,000 BTU/hr |
| 25°F | 12,500 BTU/hr |
A common rule of thumb:
For heating, 1 GPM at ΔT of 20°F ≈ 10,000 BTU/hr.
How Delta-T Affects Pipe Size (Quick Example)
Here’s the quick example I mentioned in the beginning — and it’s an important one.
Say a space needs 100,000 BTU/hr.
With a 10°F delta-T, you need:
GPM = 100,000 ÷ (500 × 10)
GPM = 20 GPM
That typically requires around 1¼-inch or 1½-inch pipe.
But if you increase delta-T to 20°F, the required GPM is cut in half:
GPM = 100,000 ÷ (500 × 20)
GPM = 10 GPM
Now the pipe size can drop to 1 inch, and the pump horsepower is lower too.
Now, while increasing delta-T can reduce your GPM, pipe size, pump horsepower, and installation cost, there is a trade-off.
A higher delta-T can sometimes increase the cost of source equipment, because boilers, chillers, and coils may need larger heat exchanger surfaces or higher supply temperatures to achieve those higher temperature drops.
So delta-T is always a design balance between piping cost and equipment cost.
Where This Formula Is Used in Real Projects
This simple relationship is crucial throughout the HVAC lifecycle:
Design Engineers
Estimators
- Validate coil schedules and mechanical plans.
- Verify that equipment capacities match design loads.
Technicians
- Diagnose low delta-T syndrome.
- Verify flow rates during commissioning.
Project Managers
- Review submittals.
- Validate change order requests involving upgraded coils, pumps, or piping.
Common Mistakes to Avoid
1. Using the wrong delta-T
Always use water temperature drop through the coil or loop, not the air temperature difference.
2. Forgetting glycol corrections
Ethylene glycol or propylene glycol reduces heat capacity.
A 30% glycol solution uses ~450 instead of 500.
3. Mixing heating and cooling delta-T
Cooling coils often use ΔT = 12–18°F
Heating coils often use ΔT = 20–30°F
Be sure you’re using the correct design values. Many existing cooling coils were designed around about 10°F ΔT, but modern high-efficiency designs – and ASHRAE 90.1 – typically push toward 15°F or higher chilled-water delta-T.
Conclusion
The ability to convert between GPM, ΔT, and BTU/hr is one of the most important hydronic skills in HVAC. Whether you’re designing a system, estimating equipment, or troubleshooting performance, this formula gives you quick insight into how much heat your hydronic loop is actually moving.
With just:
BTU/hr = 500 × GPM × ΔT,
you can size coils, validate loads, adjust flows, or calculate required GPM for any heating or cooling scenario.
