Anti-Solar Radiative Cooling Power Calculator

What this calculator estimates

Anti-solar radiative cooling is the nighttime process of rejecting heat from a surface to the cold sky by emitting longwave infrared radiation. In practical systems, a radiator (often a high-emissivity surface) cools relative to its surroundings. If a thermoelectric generator (TEG) is arranged so that one side is coupled to the radiator and the other side is coupled to a warmer heat source (often ambient air, a thermal mass, or a controlled heat sink), the temperature difference can produce electrical power. This page provides a simple, transparent estimate of the upper-bound, radiation-driven heat flow and the corresponding electrical output after applying a user-supplied conversion efficiency.

The calculator reports three main outputs:

• Net radiative cooling power from your radiator to the sky (W).
• Average electrical power after applying an overall conversion efficiency (W).
• Total nighttime energy over a chosen duration (Wh).

The model is intentionally simple: it focuses on radiative exchange between a surface at temperature T and an effective sky temperature T_sky. It does not explicitly model convection, conduction, wind, clouds, view factors, spectral selectivity, or the detailed thermodynamics of a specific TEG module. Use it for early sizing, sensitivity checks, and “what-if” comparisons (for example, how much more energy you get by increasing area versus improving conversion efficiency).

How the calculation works (formula)

The calculator uses the Stefan–Boltzmann law for a gray surface radiating to the sky. Net radiative cooling power per unit area is:

Total radiative cooling power from a radiator of area A is: Prad = A · ε · σ · (T⁴ − Tsky⁴). Electrical power is estimated using an overall thermoelectric conversion efficiency η: Pelec = η · Prad. Nighttime energy over t hours is: Enight = Pelec · t (in Wh when t is in hours).

Important constraint: the model requires T > T_sky. If the surface is not warmer than the effective sky temperature, the net radiative term becomes zero or negative and the simplified “cooling power” definition used here is not positive.

Units, definitions, and what each input means

The inputs are chosen to match the simplest radiative-cooling energy balance. Each value has a physical meaning and a practical interpretation. If you are unsure, start with conservative values, run the calculation, then adjust one parameter at a time to see which lever matters most.

Radiator area (m²)

This is the effective area that “sees” the sky and emits thermal infrared radiation. For a flat plate with an unobstructed view, the effective area is close to the physical area. For complex geometries (fins, corrugations, folded sheets), the true emitting area can be larger, but self-viewing and reduced sky view can offset that benefit. Because the calculator does not include view factors, treat the area input as the sky-facing effective area.

• Small prototypes: 0.1–2 m²
• Rooftop panels: 2–10+ m²
• Field arrays: tens to hundreds of m² (use the max limit only if you understand the assumptions)

Surface emissivity (0–1)

Emissivity describes how strongly the surface emits thermal infrared radiation compared with an ideal blackbody. In this simplified model, higher emissivity increases radiative cooling linearly. Many “radiative cooling” materials are engineered to have high emissivity in the atmospheric window (roughly 8–13 μm), but this calculator uses a single gray emissivity value. If you have spectral data, choose an emissivity that represents your material’s effective longwave emission under your conditions.

• Polished metals: ~0.05–0.2
• Painted/oxidized surfaces: ~0.8–0.95
• High-IR-emissivity coatings: ~0.95–0.99

Radiator surface temperature (K)

Enter the radiator surface temperature in kelvin. If you measure in °C, convert using K = °C + 273.15. Example: 25 °C ≈ 298 K. In a real device, the radiator temperature is not fixed; it results from a balance of radiation, convection, conduction, and any heat drawn through the TEG. Here, you provide a representative surface temperature for the period you care about.

Effective sky temperature (K)

Effective sky temperature is a compact way to represent atmospheric longwave emission back toward your radiator. It is not the same as air temperature and it is not the temperature of outer space; it is a modeling convenience that captures how “cold” the sky appears in the thermal infrared. Clear, dry nights tend to have lower T_sky (stronger cooling). Humid or cloudy nights raise T_sky (weaker cooling).

• Clear, dry night: ~220–270 K
• Typical clear conditions: ~250–290 K
• Humid/cloudy night: ~270–300 K

If you do not have a sky-temperature estimate, you can run multiple scenarios (for example 240 K, 260 K, and 280 K) to see how sensitive your design is to weather.

Thermoelectric efficiency (0–1)

This is an overall conversion factor from radiative cooling power to electrical power. It bundles TEG conversion efficiency and practical losses such as thermal contact resistance, parasitic conduction, heat spreading, and power electronics. For small temperature differences, real-world system efficiency is often only a few percent or less. If you have a TEG datasheet, remember that datasheet efficiency is typically reported under specific hot/cold-side temperatures and may not include system losses.

• Simple lab setups: ~0.01–0.05
• Well-optimized prototypes: sometimes ~0.03–0.08 depending on ΔT and design
• Values above ~0.10 are usually optimistic for this application

Night duration (hours)

Use the number of hours you expect roughly steady conditions. The calculator multiplies average electrical power by this duration to estimate energy. If conditions vary strongly through the night (clouds, wind shifts, changing humidity), consider running separate cases (early night, midnight, pre-dawn) and comparing the results. For seasonal planning, you can also run a “short night” and “long night” case to bracket expected energy.

Worked example (step-by-step)

Example scenario: a 2 m² radiator with emissivity 0.95. The radiator surface is at 300 K and the effective sky temperature is 260 K. Assume an overall thermoelectric efficiency of 0.05 and a 12-hour night.

1. Compute the radiative temperature term: T⁴ − T_sky⁴. Because 300 K is higher than 260 K, the term is positive.
2. Multiply by σ (Stefan–Boltzmann constant), emissivity, and area to get Prad in watts.
3. Multiply by efficiency η to get average electrical power Pelec.
4. Multiply by 12 hours to get nighttime energy in watt-hours.

Interpretation: if the result looks surprisingly large, it may be because the simplified model does not subtract convective heat gain from ambient air or conductive heat leaks. If the result looks very small, that can be realistic: radiative-cooling power is limited by the fourth-power temperature dependence and by the fact that the sky is not a perfect cold sink. The comparison table below the result helps you decide whether it is more effective to add radiator area or to improve conversion efficiency.

Assumptions and limitations (what to watch for)

• Radiation-only exchange: convection and conduction losses can significantly reduce real-world performance, especially in windy conditions.
• Single effective sky temperature: a single number cannot capture clouds, humidity profiles, or spectral effects; treat it as a scenario parameter.
• View to sky: nearby buildings, trees, and tilt can reduce the effective radiating view; shading and obstructions matter.
• Gray emissivity: real materials have wavelength-dependent emissivity; selective emitters may behave differently than a gray surface.
• Efficiency is lumped: η is a system-level estimate, not a guaranteed TEG module efficiency; include wiring and conversion losses if relevant.
• Average-power assumption: the calculator treats inputs as steady over the chosen duration; real nights vary.

How to use: Practical guidance for using the results

Use the outputs as a planning tool. If you are designing a device, the most useful workflow is to run a baseline case and then explore sensitivity: increase area, change emissivity, adjust sky temperature, and vary efficiency. The scenario table produced by the calculator automatically compares a baseline design to two common upgrades: a 50% area increase and a 20% efficiency increase.

When comparing designs, focus on relative changes rather than absolute numbers. For example, if doubling area roughly doubles energy in the model, that indicates area is a strong lever. In practice, doubling area may also increase structural cost, mass, and exposure to wind, and it may change the radiator temperature. Similarly, improving efficiency may require better thermal interfaces or different TEG modules, which can change the achievable temperature difference.

If you are validating against measurements, try to measure or estimate the radiator surface temperature and an effective sky temperature (or longwave downwelling radiation) during the same period. Then adjust η to match observed electrical output. That calibrated η can be used for more realistic scenario comparisons on similar nights.

Common questions and troubleshooting

Introduction: Why do I get an error about temperatures?

The calculator requires the radiator surface temperature to be at least 1 K warmer than the effective sky temperature. If you enter values where T ≤ T_sky, the net radiative term becomes non-positive. In real life, the radiator can still exchange heat with the sky, but the simplified “net cooling to sky” expression used here is intended for cases where the sky is effectively colder.

Is the “radiative flux” value per square meter?

No. In the results and table, “Radiative flux (W)” is the total radiative cooling power for the full radiator area you entered. If you want a per-area number, divide the reported radiative power by the area.

Why is the electrical power so small?

Thermoelectric conversion at small temperature differences is inherently limited. Even if the radiator rejects tens of watts of heat, only a small fraction may become electricity. Additionally, real systems lose heat through convection and conduction, which can reduce the temperature difference across the TEG.

Can I use this for daytime “anti-solar” coatings?

This calculator is specifically for nighttime longwave radiative exchange using an effective sky temperature. Daytime radiative cooling requires modeling solar absorption, atmospheric transmission, and often spectral selectivity. If you want daytime performance, you would need a different model that includes solar irradiance and the coating’s solar reflectance.