The Simple Numbers Behind Ground Source Heat Pumps
Ground source heat pump maths really comes down to three simple questions:
- How much heat will the system produce?
- How much electricity will it use?
- How much will it cost to run?
At first, this may sound complicated. However, the maths is simpler than it looks.
You do not need advanced maths or science. Instead, most calculations use simple multiplication, division, and temperature differences.
So, let’s go through the main numbers step by step.
1. Start with the Basic Units
Before looking at heat pumps, it helps to understand two basic units.
kW (Kilowatts)
kW measures power.
In simple terms, this tells you how fast heat or electricity is being delivered.
kWh (Kilowatt-hours)
kWh measures energy used over time.
In other words, this tells you how much energy you actually use.
Simple Example
Imagine a 3 kW heater running for 4 hours.
The energy used would be:
Energy = Power × Time
3 kW × 4 hours = 12 kWh
So, the heater uses:
12 kWh
A simple rule to remember is:
kW × hours = kWh
You will see this rule again and again.
2. The Key Number: COP
The most important heat pump number is COP.
COP stands for Coefficient of Performance.
Put simply, COP shows how much heat you get for each unit of electricity you use.
Formula
COP = Heat Output ÷ Electricity Input
Example
Imagine a ground source heat pump gives 8 kW of heat while using 2 kW of electricity.
The COP would be:
8 ÷ 2 = 4
This means that for every 1 unit of electricity, you get 4 units of heat.
Because the ground stays at a steady temperature, ground source heat pumps often achieve higher COP values than air source heat pumps.
3. SCOP: Average Efficiency Across the Year
COP only shows efficiency at one moment.
However, outdoor conditions change during the year.
Because of this, we also use SCOP.
SCOP stands for Seasonal Coefficient of Performance.
It shows average efficiency across a whole heating season or year.
Formula
SCOP = Total Heat Output ÷ Total Electricity Used
Example
Suppose a home needs:
- 14,000 kWh of heat each year
- 3,500 kWh of electricity
Then:
SCOP = 14,000 ÷ 3,500 = 4
So, across the year, the system gives 4 units of heat for every 1 unit of electricity.
Because ground temperature changes very little, many ground source systems achieve SCOP values of around 3.5 to 4.5.
4. Why Ground Source Heat Pumps Stay Efficient
Air temperature can rise and fall a lot.
However, ground temperature changes much less.
A few metres below the surface, the ground often stays around 8–12°C all year.
Because of this, ground source heat pumps have an easier job, especially in winter.
As a result, they usually:
- Work more efficiently
- Use less electricity
- Produce more heat
This steady heat source is one of their biggest advantages.
5. Heat Loss Drives Everything
A heat pump must replace the heat your home loses.
So, before choosing a system, you need to know how much heat your home loses.
Heat mainly escapes through:
- Walls
- Roof
- Floors
- Windows
- Ventilation
A simple formula is:
Heat Loss = U-value × Area × Temperature Difference
This helps estimate how much heating your home needs on a cold day.
6. A Simple Heat Loss Example
Suppose:
- Indoor temperature = 21°C
- Outdoor temperature = −2°C
The temperature difference is:
21 − (−2) = 23°C
Now imagine the home loses:
- 1.75 kW through walls, roof, floor, and windows
- 0.7 kW through ventilation
Total heat loss:
1.75 + 0.7 = 2.45 kW
So, on a cold winter day, this home needs about 2.5 kW of heat to stay warm.
7. Choosing Heat Pump Size
Once you know heat loss, choosing the right heat pump becomes much easier.
A simple rule is:
Heat pump output should roughly match heat loss
So, if your home loses 2.5 kW, you might look at a heat pump around 3 kW.
Installers usually also allow extra capacity for:
- Hot water
- Cold weather
- Safety margins
This helps ensure the system performs well all year.
8. Running Cost Maths
This is usually the number people care about most.
Once you know heat demand and SCOP, estimating running costs is fairly easy.
Step 1: Work Out Electricity Use
Formula:
Electricity Used = Heat Needed ÷ SCOP
Example:
Heat needed = 14,000 kWh
SCOP = 4
Electricity used:
14,000 ÷ 4 = 3,500 kWh
Step 2: Work Out Cost
Formula:
Cost = Electricity × Price per kWh
If electricity costs 25p per kWh:
3,500 × £0.25 = £875 per year
So, this gives a simple estimate of yearly running costs.
9. Flow Temperature Matters
Ground source heat pumps work best with lower water temperatures.
A simple rule is:
Lower flow temperature = Better efficiency
Higher flow temperature = Lower efficiency
That is why they often work especially well with:
- Underfloor heating
- Large radiators
These systems provide good warmth using lower water temperatures.
10. A Quick Reality Check
Suppose your home needs 6 kW of heat.
If COP = 4
Electricity needed:
6 ÷ 4 = 1.5 kW
If COP = 3
Electricity needed:
6 ÷ 3 = 2 kW
The heat needed stays the same.
However, electricity use rises by 33% when COP falls from 4 to 3.
So, even a small drop in efficiency can noticeably increase costs.
In Short
Ground source heat pump maths comes down to five key numbers:
- Heat loss (kW) — how much heat your home loses
- Heat demand (kWh) — how much energy you need over time
- COP / SCOP — system efficiency
- Electricity use (kWh) — heat demand divided by SCOP
- Running cost (£) — electricity used multiplied by price
With simple multiplication and division, you can:
- Size a system
- Compare options
- Estimate yearly running costs
The ground provides the heat.
Meanwhile, the maths helps you understand how efficiently you use it.