Global Mean Temperature Calculator
Our planetary & earth system science calculator computes global mean temperature accurately. Enter measurements for results with formulas and error
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
Te = [(S(1-a))/(4sigma)]^0.25; Ts = Te / eps^0.25; dT = lambda x (dF / 3.7)
Where Te is the effective radiating temperature, S is the solar constant (W/m2), a is albedo, sigma is the Stefan-Boltzmann constant, Ts is surface temperature adjusted for emissivity (eps), and dT is the temperature change from radiative forcing dF with climate sensitivity lambda.
Worked Examples
Example 1: Standard Earth Energy Balance
Problem:Calculate Earth's temperature with solar constant 1361 W/m2, albedo 0.30, and emissivity 0.612.
Solution:Absorbed solar = 1361 x (1 - 0.30) / 4 = 238.18 W/m2\nEffective temperature = (238.18 / 5.67e-8)^0.25 = 254.87 K = -18.28 C\nSurface temperature = 254.87 / (0.612)^0.25 = 287.97 K = 14.82 C\nGreenhouse effect = 287.97 - 254.87 = 33.10 K
Result:Surface Temp: 14.82 C | Effective Temp: -18.28 C | Greenhouse Effect: 33.10 K
Example 2: Doubled CO2 Scenario
Problem:With 3.7 W/m2 radiative forcing from CO2 doubling and climate sensitivity of 3.0 C, estimate the new temperature.
Solution:Starting surface temp = 287.97 K (14.82 C)\nTemperature change = 3.0 x (3.7 / 3.7) = 3.0 C\nNew surface temp = 287.97 + 3.0 = 290.97 K = 17.82 C\nThis represents the equilibrium warming after all feedbacks have fully responded.
Result:New Surface Temp: 17.82 C | Warming: +3.0 C above pre-industrial baseline
Frequently Asked Questions
What is the global mean temperature and how is it calculated?
The global mean temperature is the average temperature of Earth's surface, currently about 15 degrees Celsius (288 K). It is calculated using an energy balance model where incoming solar radiation must balance outgoing thermal radiation. The Sun delivers about 1,361 watts per square meter at Earth's orbit, but only one quarter of this is intercepted by the cross-sectional area of Earth. After accounting for reflected sunlight (albedo of about 30 percent), the absorbed energy determines the equilibrium temperature through the Stefan-Boltzmann law, modified by the greenhouse effect.
What is the Stefan-Boltzmann law and how does it apply to Earth's temperature?
The Stefan-Boltzmann law states that a blackbody radiates energy proportional to the fourth power of its absolute temperature, with the proportionality constant sigma equal to 5.67 times 10 to the negative eighth watts per square meter per Kelvin to the fourth. For Earth, this law determines the effective radiating temperature, which is the temperature Earth would be if it had no atmosphere (about 255 K or minus 18 degrees Celsius). The actual surface temperature is higher because the atmosphere absorbs and re-emits infrared radiation, creating the greenhouse effect that warms the surface by approximately 33 degrees Celsius.
What is planetary albedo and how does it affect temperature?
Planetary albedo is the fraction of incoming solar radiation that is reflected back to space without being absorbed. Earth's average albedo is approximately 0.30, meaning 30 percent of sunlight is reflected by clouds, ice sheets, deserts, and aerosols. Higher albedo means less absorbed energy and lower temperatures. Ice ages increase albedo through expanded ice sheets, creating a positive feedback loop that further cools the planet. Conversely, melting Arctic ice reduces albedo, causing more solar absorption and additional warming. Even a small change in albedo of 0.01 can shift global temperature by roughly 0.5 to 1.0 degrees Celsius.
What is radiative forcing and how does it drive temperature change?
Radiative forcing is the change in net energy flux at the tropopause caused by an external perturbation such as increased greenhouse gas concentrations. It is measured in watts per square meter. A doubling of atmospheric CO2 produces a radiative forcing of approximately 3.7 watts per square meter, which is the standard benchmark used in climate science. Positive forcing causes warming while negative forcing causes cooling. Total anthropogenic forcing since pre-industrial times is estimated at about 2.7 watts per square meter, combining the warming effects of greenhouse gases with the partially offsetting cooling effect of aerosol pollution.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy