The Simple Numbers Behind Solar Panels
Solar panel maths comes down to one simple question:
How much electricity can we make from sunlight?
At first, this may sound technical.
However, the maths is simpler than many people expect.
Most solar calculations use only:
- Multiplication
- Division
- Percentages
So, let’s build the maths step by step.
1. Start with Sunlight Power
First, solar panels need sunlight.
The strength of sunlight is called solar irradiance.
This simply means how much solar power is hitting a surface.
It is measured in:
Watts per square metre (W/m²)
Example
A bright sunny day around midday may reach:
1,000 W/m²
This is often used as a standard test level.
At this stage, there is no maths yet.
We are simply measuring sunlight.
2. Power vs Energy
This is one of the most important ideas in solar maths.
Power (W or kW)
Power tells you how fast electricity is being produced right now.
Energy (Wh or kWh)
Energy tells you how much electricity is produced over time.
Key Rule
Energy = Power × Time
Or:
kWh = kW × Hours
Example
If your solar system produces 2 kW for 3 hours:
Energy = 2 × 3 = 6 kWh
So, the system generates:
6 kWh of electricity
You will see this rule again and again.
3. What Panel Power Ratings Mean
Solar panels come with a power rating.
This is usually written as Wp, which means watts peak.
This tells you the panel’s maximum output in ideal conditions.
For example:
A 400 W panel can produce:
400 watts
—but only under perfect test conditions.
These test conditions include:
- Strong sunlight (1,000 W/m²)
- Panel temperature of 25°C
- Ideal testing conditions
In real life, output changes because sunlight, temperature, and panel angle all change.
4. The Main Solar Power Equation
A simple solar power equation is:
Panel Power = Sunlight × Panel Area × Efficiency
This helps estimate how much power a panel can produce.
Example
Suppose:
- Sunlight = 700 W/m²
- Panel area = 1.8 m²
- Efficiency = 20% (0.20)
Calculation:
700 × 1.8 × 0.20 = 252 W
So the panel produces about:
252 watts
This explains why a 400 W panel often produces less than 400 W.
Real conditions are rarely perfect.
5. System Size (kWp)
When many panels are connected together, installers talk about system size.
This is usually measured in kWp.
kWp means:
Kilowatt peak
In simple terms, this is the maximum power the full system could produce in ideal conditions.
Example
Suppose you have:
- 10 panels
- Each rated at 400 W
Total power:
10 × 400 = 4,000 W
That equals:
4.0 kWp
Many UK home systems are around this size.
6. Estimating Yearly Output
A quick way to estimate yearly generation is:
Annual Energy ≈ System Size × Annual Yield
Example
Suppose:
- System size = 4.5 kWp
- Expected yearly output = 2,850 kWh
To find annual yield:
2,850 ÷ 4.5 = 633
That gives:
633 kWh per kWp per year
However, this varies a lot depending on:
- Location
- Roof direction
- Roof angle
- Shading
- Weather
So yearly output is always an estimate, not a guarantee.
7. Real-World Losses
Even with strong sunlight, real systems lose some energy.
Common losses include:
- Inverter losses
- Heat losses
- Cable losses
- Dirt on panels
- Shading
A simple way to allow for losses is Performance Ratio (PR).
A well-designed system often has a PR of around:
0.8 (80%)
This means the system produces about 80% of ideal output.
Simple Rule
Real Output = Ideal Output × PR
Example
If ideal output is:
3,500 kWh/year
And PR is:
0.8
Then:
3,500 × 0.8 = 2,800 kWh/year
So real output becomes:
2,800 kWh per year
8. Roof Direction and Angle Matter
Solar panels work best when sunlight hits them directly.
A simple rule is:
More direct sunlight = More power
More sideways sunlight = Less power
Because of this, roof direction and tilt matter a lot.
Panels facing the sun for longer usually generate more electricity.
Shading can also reduce output significantly.
In Short
Most solar panel maths comes down to five key things:
- Sunlight strength (W/m²)
- System size (kWp)
- Time (hours)
- Energy losses
- Yearly output (kWh/year)
That is really all you need.
Once you understand these numbers, solar panel maths becomes much easier.
And remember the most important rule:
kW × hours = kWh