Input Parameters
Fill the fields below, then press Calculate. Optional fields help with net radiation and equilibrium temperature checks.
Formula Used
This calculator uses the Stefan–Boltzmann law for longwave thermal emission: F = ε σ T⁴, where F is radiative flux (W/m²), ε is emissivity, σ is 5.670374419×10⁻⁸ W·m⁻²·K⁻⁴, and T is temperature in kelvin.
If a background temperature is provided, net longwave exchange is: Fnet = ε σ (Ts⁴ − Tbg⁴). Total power follows P = F · A, using area in m².
Peak emission wavelength uses Wien’s displacement law: λmax = b / T, with b = 2.897771955×10⁻³ m·K (reported in µm).
How to Use This Calculator
- Enter the surface temperature and choose units.
- Set emissivity for the surface material, from 0 to 1.
- Enter the emitting area to compute total emitted power.
- Optionally add a background temperature to estimate net loss.
- Optionally enter absorbed flux to compute equilibrium temperature.
- Press Calculate to view results above the form.
Example Data Table
Values below are illustrative. Flux uses F = εσT⁴ and λmax uses b/T.
| Surface T (K) | ε | Area (m²) | Flux (W/m²) | Power (W) | λmax (µm) |
|---|---|---|---|---|---|
| 288 | 0.96 | 1 | 374.50 | 374.50 | 10.06 |
| 300 | 0.98 | 10 | 450.11 | 4,501.14 | 9.66 |
| 273.15 | 0.95 | 5 | 299.87 | 1,499.37 | 10.61 |
| 310 | 0.97 | 2 | 507.96 | 1,015.92 | 9.35 |
| 255 | 1.00 | 1 | 239.76 | 239.76 | 11.36 |
Blackbody Radiation at Earth’s Surface
1) Why surface emission matters
Earth’s surface continuously emits thermal infrared energy. This emission is a key term in surface energy balance, alongside absorbed sunlight, turbulent heat exchange, and atmospheric back‑radiation. When you quantify outgoing longwave flux, you can compare surfaces, seasons, and scenarios using one consistent physical rule. These estimates are also useful for sanity checks against infrared observations and surface energy‑budget diagrams.
2) Stefan–Boltzmann scaling
The Stefan–Boltzmann law uses F = εσT⁴. The T⁴ dependence is powerful: a small temperature increase can noticeably raise emission. For example, changing from 288 K to 300 K increases T⁴ enough to lift flux by tens of W/m² even when emissivity remains near 1. That sensitivity explains strong heat‑wave impacts on nighttime cooling rates.
3) Typical Earth reference numbers
A common near‑surface reference is 288 K (about 15 °C). With emissivity around 0.96, the calculator yields roughly 374 W/m² of emitted flux for a 1 m² patch. In contrast, the planet’s effective radiating temperature near 255 K corresponds to about 240 W/m², illustrating atmospheric greenhouse influence.
4) Emissivity and real materials
Emissivity encodes how closely a surface behaves like an ideal emitter. Many soils, water, vegetation, and building materials lie between 0.90 and 0.99. Lower emissivity reduces longwave output at the same temperature, which is why surface type matters in remote sensing and urban heat studies.
5) Peak wavelength and infrared context
Wien’s law (λmax = b/T) links temperature to the peak of the thermal spectrum. Around 288 K, the peak is near 10 µm, firmly in the infrared. This region overlaps with atmospheric absorption bands, so radiation leaving the surface may be absorbed and re‑emitted by the air. Colder surfaces shift the peak to longer wavelengths, hotter surfaces shift it shorter.
6) Net longwave using a background temperature
The optional background temperature approximates longwave exchange with the overlying environment using Fnet = εσ(Ts⁴ − Tbg⁴). If the background is warmer than the surface, net flux can become negative, indicating the surface gains longwave energy instead of losing it.
7) Equilibrium temperature check from absorbed flux
If you enter absorbed flux, the tool estimates equilibrium temperature from T = (F/(εσ))¹ᐟ⁴. This is useful for quick “what‑if” comparisons: increase absorbed energy, and the equilibrium temperature rises; increase emissivity, and equilibrium temperature falls for the same absorbed flux.
8) Practical modeling tips
For flux‑only comparisons, set area to 1 m². Use realistic emissivity for your surface, and keep temperatures in kelvin for physical checks. For climate‑style sketches, pair the absorbed‑flux option with a background temperature to separate “surface emission” from “net to atmosphere” behavior. For time‑series work, run several temperatures (day/night or seasonal), export CSV, and plot flux versus temperature to visualize the T⁴ sensitivity.
FAQs
1) What does this calculator output?
It returns emitted flux (W/m²), total power (W) for your chosen area, peak wavelength (µm), optional net longwave flux with a background temperature, and an optional equilibrium temperature from absorbed flux.
2) Why must temperature be in kelvin internally?
The Stefan–Boltzmann law uses absolute temperature. Converting °C or °F to kelvin prevents unphysical values and ensures T⁴ scaling is computed correctly.
3) What emissivity should I use for Earth surfaces?
Many natural surfaces are high: water and vegetation are often ~0.96–0.99, while dry soils and rocks can be ~0.90–0.98. Use a value appropriate to your material and wavelength band.
4) What does background temperature represent?
It approximates the effective infrared temperature of the surrounding environment (such as sky or atmosphere) that exchanges longwave energy with the surface, enabling a simple net‑radiation estimate.
5) How do I use the absorbed flux option?
Enter absorbed energy in W/m² (for example, absorbed sunlight minus reflected). The calculator estimates the temperature that would emit the same flux, given the emissivity you selected.
6) Why is peak wavelength important?
It indicates where the thermal spectrum is strongest. Around typical Earth temperatures, the peak is near 10 µm, which helps interpret infrared measurements and atmospheric absorption effects.
7) Does this replace a full climate model?
No. It is an idealized radiation calculator. Real conditions also involve clouds, humidity, convection, latent heat, and spectral emissivity variations. Use it for quick checks and comparisons.