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Solar Panel worksheet

Grades 6–7 · CCSS 6.RP.A.3.b, 6.RP.A.3.c

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- What do you want to find?: Production of a system
- System size (DC rating): 6 kW
- Peak sun hours per day (example: 4.5): 4.8 h/day
- System efficiency / derate factor (typical: 80%): 95%
- Panel wattage (example: 400 W): 300 W
Find: Estimated annual production
Answer
2.
Problem 2.
- What do you want to find?: System size for my usage
- Electricity use: 875 kWh per month
- Share of that use to cover with solar: 90%
- Peak sun hours per day (example: 4.5): 4 h/day
- System efficiency / derate factor (typical: 80%): 90%
- Panel wattage (example: 400 W): 500 W
Find: System size needed
Answer
3.
Problem 3.
- What do you want to find?: System size for my usage
- Electricity use: 740 kWh per month
- Share of that use to cover with solar: 100%
- Peak sun hours per day (example: 4.5): 4.6 h/day
- System efficiency / derate factor (typical: 80%): 100%
- Panel wattage (example: 400 W): 550 W
Find: System size needed
Answer
4.
Problem 4.
- What do you want to find?: Production of a system
- System size (DC rating): 7 kW
- Peak sun hours per day (example: 4.5): 5.5 h/day
- System efficiency / derate factor (typical: 80%): 90%
- Panel wattage (example: 400 W): 480 W
Find: Estimated annual production
Answer
5.
Problem 5.
- What do you want to find?: System size for my usage
- Electricity use: 700 kWh per month
- Share of that use to cover with solar: 90%
- Peak sun hours per day (example: 4.5): 4.2 h/day
- System efficiency / derate factor (typical: 80%): 75%
- Panel wattage (example: 400 W): 330 W
Find: System size needed
Answer
6.
Problem 6.
- What do you want to find?: System size for my usage
- Electricity use: 950 kWh per month
- Share of that use to cover with solar: 90%
- Peak sun hours per day (example: 4.5): 6 h/day
- System efficiency / derate factor (typical: 80%): 45%
- Panel wattage (example: 400 W): 460 W
Find: System size needed
Answer
7.
Problem 7.
- What do you want to find?: System size for my usage
- Electricity use: 1,250 kWh per month
- Share of that use to cover with solar: 70%
- Peak sun hours per day (example: 4.5): 4.5 h/day
- System efficiency / derate factor (typical: 80%): 100%
- Panel wattage (example: 400 W): 320 W
Find: System size needed
Answer
8.
Problem 8.
- What do you want to find?: Production of a system
- System size (DC rating): 6 kW
- Peak sun hours per day (example: 4.5): 4 h/day
- System efficiency / derate factor (typical: 80%): 75%
- Panel wattage (example: 400 W): 425 W
Find: Estimated annual production
Answer
9.
Problem 9.
- What do you want to find?: System size for my usage
- Electricity use: 1,120 kWh per month
- Share of that use to cover with solar: 100%
- Peak sun hours per day (example: 4.5): 4.5 h/day
- System efficiency / derate factor (typical: 80%): 75%
- Panel wattage (example: 400 W): 500 W
Find: System size needed
Answer
10.
Problem 10.
- What do you want to find?: System size for my usage
- Electricity use: 750 kWh per month
- Share of that use to cover with solar: 90%
- Peak sun hours per day (example: 4.5): 3.9 h/day
- System efficiency / derate factor (typical: 80%): 74%
- Panel wattage (example: 400 W): 350 W
Find: System size needed
Answer

Answer key: Solar Panel worksheet

1. Estimated annual production: 9,986 kWh/yr
1. Find the daily output: each kW makes 1 kWh per peak sun hour, minus the losses
  $6 kW \times 4.8 h \times 0.95$ $= 27.36 kWh$
2. Multiply by 365 days to get the yearly output
  $27.36 kWh \times 365$ $= 9,986.4 kWh$
3. Split the yearly output into 12 for an average month
  $\frac{9,986.4 kWh}{12}$ $= 832.2 kWh$
4. Count the panels: the size in watts divided by each panel's watts, rounded up because panels come whole
  $\frac{6,000 W}{300 W}$ $= 20$ $= →$ $= 20$
2. System size needed: 7.19 kW
1. Turn your monthly use into a yearly total: monthly use × 12
  $875 kWh \times 12$ $= 10,500 kWh$
2. Find how much of that you want solar to make: yearly use × the share to cover
  $10,500 kWh \times 90%$ $= 9,450 kWh$
3. Spread the yearly target over 365 days, because sun hours are given per day
  $\frac{9,450 kWh}{365}$ $= 25.8904 kWh$
4. Divide by the useful sun hours each day (sun hours × efficiency) to get the system size in kW
  $\frac{25.8904 kWh}{4 h \times 0.9}$ $= 7.1918 kW$
5. Count the panels: the size in watts divided by each panel's watts, rounded up because panels come whole
  $\frac{7,191.78 W}{500 W}$ $= 14.384$ $= →$ $= 15$
3. System size needed: 5.29 kW
1. Turn your monthly use into a yearly total: monthly use × 12
  $740 kWh \times 12$ $= 8,880 kWh$
2. Spread the yearly target over 365 days, because sun hours are given per day
  $\frac{8,880 kWh}{365}$ $= 24.3288 kWh$
3. Divide by the useful sun hours each day (sun hours × efficiency) to get the system size in kW
  $\frac{24.3288 kWh}{4.6 h \times 1}$ $= 5.2889 kW$
4. Count the panels: the size in watts divided by each panel's watts, rounded up because panels come whole
  $\frac{5,288.86 W}{550 W}$ $= 9.616$ $= →$ $= 10$
4. Estimated annual production: 12,647 kWh/yr
1. Find the daily output: each kW makes 1 kWh per peak sun hour, minus the losses
  $7 kW \times 5.5 h \times 0.9$ $= 34.65 kWh$
2. Multiply by 365 days to get the yearly output
  $34.65 kWh \times 365$ $= 12,647.25 kWh$
3. Split the yearly output into 12 for an average month
  $\frac{12,647.25 kWh}{12}$ $= 1,053.94 kWh$
4. Count the panels: the size in watts divided by each panel's watts, rounded up because panels come whole
  $\frac{7,000 W}{480 W}$ $= 14.583$ $= →$ $= 15$
5. System size needed: 6.58 kW
1. Turn your monthly use into a yearly total: monthly use × 12
  $700 kWh \times 12$ $= 8,400 kWh$
2. Find how much of that you want solar to make: yearly use × the share to cover
  $8,400 kWh \times 90%$ $= 7,560 kWh$
3. Spread the yearly target over 365 days, because sun hours are given per day
  $\frac{7,560 kWh}{365}$ $= 20.7123 kWh$
4. Divide by the useful sun hours each day (sun hours × efficiency) to get the system size in kW
  $\frac{20.7123 kWh}{4.2 h \times 0.75}$ $= 6.5753 kW$
5. Count the panels: the size in watts divided by each panel's watts, rounded up because panels come whole
  $\frac{6,575.34 W}{330 W}$ $= 19.925$ $= →$ $= 20$
6. System size needed: 10.41 kW
1. Turn your monthly use into a yearly total: monthly use × 12
  $950 kWh \times 12$ $= 11,400 kWh$
2. Find how much of that you want solar to make: yearly use × the share to cover
  $11,400 kWh \times 90%$ $= 10,260 kWh$
3. Spread the yearly target over 365 days, because sun hours are given per day
  $\frac{10,260 kWh}{365}$ $= 28.1096 kWh$
4. Divide by the useful sun hours each day (sun hours × efficiency) to get the system size in kW
  $\frac{28.1096 kWh}{6 h \times 0.45}$ $= 10.411 kW$
5. Count the panels: the size in watts divided by each panel's watts, rounded up because panels come whole
  $\frac{10,410.96 W}{460 W}$ $= 22.633$ $= →$ $= 23$
7. System size needed: 6.39 kW
1. Turn your monthly use into a yearly total: monthly use × 12
  $1,250 kWh \times 12$ $= 15,000 kWh$
2. Find how much of that you want solar to make: yearly use × the share to cover
  $15,000 kWh \times 70%$ $= 10,500 kWh$
3. Spread the yearly target over 365 days, because sun hours are given per day
  $\frac{10,500 kWh}{365}$ $= 28.7671 kWh$
4. Divide by the useful sun hours each day (sun hours × efficiency) to get the system size in kW
  $\frac{28.7671 kWh}{4.5 h \times 1}$ $= 6.3927 kW$
5. Count the panels: the size in watts divided by each panel's watts, rounded up because panels come whole
  $\frac{6,392.69 W}{320 W}$ $= 19.977$ $= →$ $= 20$
8. Estimated annual production: 6,570 kWh/yr
1. Find the daily output: each kW makes 1 kWh per peak sun hour, minus the losses
  $6 kW \times 4 h \times 0.75$ $= 18 kWh$
2. Multiply by 365 days to get the yearly output
  $18 kWh \times 365$ $= 6,570 kWh$
3. Split the yearly output into 12 for an average month
  $\frac{6,570 kWh}{12}$ $= 547.5 kWh$
4. Count the panels: the size in watts divided by each panel's watts, rounded up because panels come whole
  $\frac{6,000 W}{425 W}$ $= 14.118$ $= →$ $= 15$
9. System size needed: 10.91 kW
1. Turn your monthly use into a yearly total: monthly use × 12
  $1,120 kWh \times 12$ $= 13,440 kWh$
2. Spread the yearly target over 365 days, because sun hours are given per day
  $\frac{13,440 kWh}{365}$ $= 36.8219 kWh$
3. Divide by the useful sun hours each day (sun hours × efficiency) to get the system size in kW
  $\frac{36.8219 kWh}{4.5 h \times 0.75}$ $= 10.9102 kW$
4. Count the panels: the size in watts divided by each panel's watts, rounded up because panels come whole
  $\frac{10,910.2 W}{500 W}$ $= 21.82$ $= →$ $= 22$
10. System size needed: 7.69 kW
1. Turn your monthly use into a yearly total: monthly use × 12
  $750 kWh \times 12$ $= 9,000 kWh$
2. Find how much of that you want solar to make: yearly use × the share to cover
  $9,000 kWh \times 90%$ $= 8,100 kWh$
3. Spread the yearly target over 365 days, because sun hours are given per day
  $\frac{8,100 kWh}{365}$ $= 22.1918 kWh$
4. Divide by the useful sun hours each day (sun hours × efficiency) to get the system size in kW
  $\frac{22.1918 kWh}{3.9 h \times 0.74}$ $= 7.6895 kW$
5. Count the panels: the size in watts divided by each panel's watts, rounded up because panels come whole
  $\frac{7,689.46 W}{350 W}$ $= 21.97$ $= →$ $= 22$