How much energy is in the sunlight that reaches Earth?
― One hour of it is almost enough to cover humanity's whole year
Step out into the sun and your face slowly warms up. Turn that warmth into numbers, and the amount is bigger than you'd expect. On a sunny midday, the light landing on just one square metre of ground is about as much power as an electric kettle. Add that up across the whole planet, and in a single hour it comes to almost as much energy as humanity uses in an entire year.
It's a clear autumn lunch break. You're sitting on a bench, soaking up the sun. The breeze is a little cool, but the patch of your back facing the sun feels warm.
A cloud drifts across the sun, and suddenly you feel chilly. Once the cloud passes, the warmth comes right back.
That warmth is the energy of light that has just finished a 150-million-kilometre journey. So how much energy, exactly, are we talking about?
There are only two reasons the number ends up so huge
On a clear day with the sun high overhead, about 1000 watts of light reaches each square metre of ground — roughly the pull of an electric kettle or a hair dryer.
The area Earth uses to catch sunlight is about 127 million square kilometres. Light pours onto the whole of it, non-stop, day and night.
"The amount per square metre" and "the area that catches it." Multiply just these two together, and you get a startlingly large number. Let's go through it step by step.
One square metre receives about as much as an electric kettle
Just outside Earth's atmosphere, a one-square-metre panel aimed straight at the sun receives about 1361 joules of light every second. This is called the solar constant. 1361 joules per second means 1361 watts.
Passing through the air, some of that light gets reflected or absorbed. So on a clear day, when the sun is nearly overhead, about 1000 watts per square metre actually reaches the ground. Solar panel performance is also measured against this "1000 watts" benchmark.
But that's only true when the sun is high. Look at Figure 1. When the sun is low, the same width of light gets stretched out over a longer stretch of ground. The total amount of light is unchanged, but it's spread thinly over a wider area, so the amount per square metre drops.
In Tokyo, the sun's midday height is about 78 degrees around the summer solstice and about 31 degrees around the winter solstice. Compared per square metre of ground, winter midday light is only about half of summer's. Winter isn't cold because the sun is farther away — it's because the light hits at an angle and spreads out thin.
Across the whole Earth: one hour equals humanity's whole year
Next, let's think about the light the whole Earth catches. The sun is so far away that the light reaching Earth arrives essentially as parallel rays. Look at Figure 2. Earth is a sphere, but from the light's point of view, it's as if a single "disc" with the same radius as Earth is blocking the light.
This disc's area is about 127 million square kilometres. Outside the atmosphere, light at 1361 watts per square metre keeps falling on it. Multiply them together, and Earth catches about 170 million gigawatts of light. If one large power station is about one gigawatt, that's equivalent to 170 million of them.
Gather up one hour's worth of that light and it comes to about 620 exajoules (exa is 10 to the 18th power). The whole world's people are estimated to use around 600 exajoules of energy per year. In other words, one hour of sunlight reaching Earth is almost the same as humanity's energy use for an entire year.
The reason is "thinness." Light arrives spread thinly over an enormous area. Averaged across the whole Earth — day and night, equator and poles — it comes to about 340 watts per square metre outside the atmosphere (a quarter of 1361 watts). On top of that, about 30% of it is bounced straight back into space by clouds and ice. Even plants are estimated to convert only around 1% of the light that reaches them into nutrients. Collecting it is the hard part.
Summary
The sunlight reaching one square metre of ground is about as much as an electric kettle on a clear midday. Earth catches this non-stop with a disc of 127 million square kilometres. As a result, just one hour of that light is enough to match the energy humanity uses in a whole year. At the same time, light hitting at an angle spreads thin, and that's also where seasonal hot and cold comes from.
Sunlight, in sheer quantity, is more than enough.
The hard part is gathering it back up once it has spread thin.
For how hot the ground gets in direct sun, see "Why does asphalt get hotter than 60°C?" and "Why does the inside of a car parked in the sun get so hot?"; for how the sun's angle relates to the seasons, see "How the seasons work."
- On a sunny day, hold your palm facing straight at the sun for about 30 seconds and feel the warmth.
- Now tilt your palm so the light just grazes it at an angle. It should feel noticeably weaker than before.
- Stand a 1-metre stick upright on the ground and measure its shadow. If the shadow is the same length as the stick, the sun is at 45 degrees; the shorter the shadow, the higher the sun.
Never look directly at the sun — it can damage your eyes. Compare the shadow length in summer and winter, and you can see the difference shown in Figure 1 with your own eyes.
Want to go deeper? ― Terms, formulas, and how this connects to the textbooksWe mark which level each part belongs to, from middle-school science to university specialist subjects
- MSCovered in middle-school science
- HSCovered in high-school "Physics" or "Earth Science"
- HS+High-school advanced content, or textbook sidebar material
- UnivNot covered in high school — a university specialist subject (meteorology, atmospheric radiation)
- ResearchNot yet settled even at university level — something researchers are still investigating
MSTerms: this phenomenon has names
- Solar constant: the energy of light received per second by a one-square-metre surface perpendicular to the sun, just outside Earth's atmosphere. Estimated at about 1361 watts per square metre.
- Solar radiation (insolation): the energy of light arriving from the sun. The value measured at the ground is called "irradiance," and is also observed at weather stations.
- Solar altitude at culmination: the angle above the horizon when the sun reaches its highest point of the day. It changes with the seasons.
MSHSCheck it with a formula: the energy Earth receives in one hour
We find the total amount of light Earth catches from the disc's area and the solar constant. The symbols mean the following.
| Symbol | Meaning and unit |
| P | Power of light Earth receives (watts) |
| S | Solar constant (watts per square metre) |
| R | Earth's radius (metres) |
| E | Energy received over time t (joules) |
| In symbols | P = S × π × R² 、 E = P × t |
| In words | Light received = light per square metre × disc area (pi × radius × radius); energy = power × time |
| Where this comes from | The area blocking parallel light equals the area of the sphere's "shadow" circle (Figure 2). Energy equals power multiplied by time, by definition. |
| Solar constant S | 1361 watts per square metre |
| Earth's radius R | 6370 kilometres |
| 1 square kilometre | 1,000,000 square metres |
| 1 hour | 3600 seconds |
| World annual energy consumption | estimated around 600 exajoules |
| Radius × radius (square kilometres) | 6370 × 6370 = 40,576,900 |
| Disc area (square kilometres) | 40,576,900 × 3.14 ≒ 127,000,000 |
| Light per square kilometre (watts) | 1361 × 1,000,000 = 1,361,000,000 |
| Same amount in gigawatts | 1,361,000,000 ÷ 1,000,000,000 ≒ 1.36 |
| Total light P for whole Earth (gigawatts) | 127,000,000 × 1.36 ≒ 172,700,000 |
| One hour's worth (gigajoules) | 172,700,000 × 3600 ≒ 621,700,000,000 |
| Converted to exajoules | 621,700,000,000 ÷ 1,000,000,000 ≒ 622 |
Earth receives about 622 exajoules of light per hour — almost the same as humanity's annual consumption (around 600 exajoules).
| Light on one tatami mat (about 1.6 square metres) at sunny midday (watts) | 1000 × 1.6 = 1600 |
| Tokyo at winter-solstice midday (sine of 31° sun height is about 0.52) | 1000 × 0.52 = 520 |
A sunlit tatami mat receives a bit more light than one electric kettle's worth. At winter-solstice midday, the light per square metre of the same ground drops to about half (this is the same simplified calculation as in Figure 1).
HSHS+Angle, and Earth's overall average
HSWhen light hits the ground at an angle, the amount per square metre shrinks in proportion to the "sine of the sun's height." That's the formula in Figure 1 (1000 watts × sine). The seasonal change in the sun's height is the main reason summer and winter differ in temperature.
HS+A sphere's surface area is four times the area of its disc, so averaged across the whole Earth, the light works out to a quarter of the solar constant — about 340 watts per square metre. About 30% of this (the albedo) is reflected back, and the rest warms the Earth. From this balance, Earth's "radiative equilibrium temperature" works out to about minus 18°C. The fact that the real average temperature is about 15°C is due to the greenhouse effect.
UnivThe path through the atmosphere, and air mass
In reality, the lower the sun, the longer and more slanted the path the light takes through the atmosphere, and the more it's weakened by scattering and absorption. This path length, expressed relative to light coming straight down (taken as 1), is called "air mass." How light weakens as it passes through the atmosphere is described by the Beer-Lambert law. The calculation in Figure 1 is a simplification that leaves this effect out. The overall exchange of light for the whole Earth is treated, as "Earth's energy budget," in atmospheric radiation science.
📖 For the derivation of the formulas and further reading: Solar constant (Wikipedia, Japanese) ／ Beer-Lambert law (Wikipedia, Japanese)
ResearchWhat's still not fully understood
- The precise value of the solar constant Satellite observations led to a revision in the 2000s from about 1365 down to about 1361 watts per square metre. Work to verify discrepancies between different instruments is still ongoing.
- Long-term changes in the sun's brightness The sun's brightness varies slightly on an roughly 11-year cycle, but how large the variation is over centuries-long timescales isn't clearly known.
- How much light clouds reflect How large a share of light Earth reflects depends heavily on clouds, and how clouds will change with warming is considered one of the biggest sources of uncertainty in climate projections.
In other words, this article too is an explanation "within the limits of what's currently known." Please take the figures as a guide for understanding the mechanism, not as exact values.
How this connects to the textbooks (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| MS | 3rd-year science, "Earth and Space" (seasonal change and solar altitude at culmination), electric power and energy | Figure 1, amount of winter vs. summer light |
| HS | Basic Earth Science, "Earth's heat budget"; Basic Physics, "Energy" | Calculation of light received by whole Earth |
| HS+ | Earth Science, "radiative equilibrium" | The quarter average and albedo |
| Univ | Meteorology, atmospheric radiation science | Air mass, Beer-Lambert law |
| Research | Satellite observation of solar radiation, clouds and climate | Revision of the solar constant, effect of clouds |
| ― | Connections to daily life | Sunbathing, seasonal hot and cold, solar panels |
- Kopp, G. and Lean, J. L. (2011) A new, lower value of total solar irradiance: Evidence and climate significance. Geophysical Research Letters 38
- Solar constant (太陽定数) - Wikipedia Japan
- Solar radiation / insolation (日射) - Wikipedia Japan
- National Astronomical Observatory of Japan (国立天文台), ed., Rika Nenpyo (Chronological Scientific Tables), Maruzen Publishing (solar constant and Earth's radius)
- Energy Institute, Statistical Review of World Energy (world primary energy consumption)
※This article is a general-audience science explainer. The figures given are approximate, meant to help you understand the mechanism. Never look directly at the sun.