Home > Solar luminosity

It is equal to the luminosity of the Sun, which is 3.9 × 10²⁶ W.

Calculating with this constant

You can calculate how much solar power hits the Earth by comparing a cross sectional area of the Earth and the total surface area of a sphere with a radius equal to the distance of the earth from the sun.

• The Earth's radius is 3963 miles (6,378 km).
• The Earth's cross sectional area = π×radius² = 49.3 million square miles (128,000,000 km²).
• The Sun's average distance is about 93 million miles (150,000,000 km).
• The surface area of a sphere = 4×π×radius² = 1.09×10¹⁷ square miles (2.82×10¹⁷ km²).
• Power reaching the Earth = P(total) × Area(earth)/Area(sphere) = 1.77×10¹⁷ W.
• The power hitting a square meter of area on Earth: (square meter = 1/1609² square miles)
  • Power over square meter = P(total)(1/1609²)/area(sphere) = 1387 W (the solar constant)
• Estimates have been made that humans use about 12×10¹² W.
• How much land area would be needed to power that?
  • The best solar cells can produce about 33% efficiency.
  • Area needed = 12×10¹²/1387/0.33 = 26×1⁹ m² = 10122 square miles ~100×100 mile square. (More needed since Sun not always straight over head nor always sunny skies, and also some fraction radiation does not reach the surface.)