Stefan–Boltzmann Net Longwave Radiation Calculator

Compute outgoing and incoming longwave flux using temperatures. Include emissivity and effective sky radiation effects. Compare scenarios, export reports, and validate climate calculations easily.

Use Stefan–Boltzmann when you have temperatures and emissivities. Use direct mode when you already know L↓ and L↑.
Typical land surfaces: 0–60 °C.
Often approximated using near‑surface air temperature.
Water/vegetation ~0.97–0.99. Dry soil ~0.90–0.97.
Brutsaert estimation is useful when emissivity is unknown.
Clear sky often ~0.70–0.90. Cloudy skies approach 1.00.
Typical near-surface: ~0.5–3.5 kPa.
0 = clear; 1 = overcast. Used to increase εsky.
W/m²
Atmospheric longwave received by the surface.
W/m²
Surface thermal emission leaving the surface.

Formula used

This tool uses the Stefan–Boltzmann law for thermal radiation flux: L = ε σ T⁴, where σ = 5.670374419×10⁻⁸ W·m⁻²·K⁻⁴, ε is emissivity, and T is absolute temperature (K).

If you choose Brutsaert estimation, the clear-sky emissivity is approximated as εclear = 1.24 (ea / T)^(1/7) (ea in kPa, T in K), then blended with cloud fraction C toward ε ≈ 1.

How to use this calculator

  1. Pick a mode: Stefan–Boltzmann for temperatures, or direct fluxes.
  2. Enter surface temperature and an effective sky temperature.
  3. Set surface emissivity, then choose a sky emissivity option.
  4. Click Calculate to see results above the form.
  5. Use CSV/PDF buttons to export your computed values.

Example data table

Ts (°C) Tsky (°C) εs εsky L↓ (W/m²) L↑ (W/m²) Rnl = L↓ − L↑ (W/m²)
20 10 0.98 0.85 309.811 410.391 -100.580
35 25 0.97 0.90 403.268 495.943 -92.676
5 -5 0.99 0.75 219.879 336.018 -116.139

Negative net values indicate a longwave loss from the surface.

Stefan–Boltzmann Net Longwave Radiation Guide

1) Why net longwave radiation matters

Net longwave radiation (Rnl) is the balance between atmospheric longwave energy reaching the surface and thermal emission leaving it. It is a key term in surface energy budgets, influencing night-time cooling, frost risk, and sensible and latent heat fluxes in micrometeorology.

2) What the calculator outputs

The calculator reports downward longwave (L↓), upward longwave (L↑), and net longwave (Rnl = L↓ − L↑) in W/m². It also converts each flux to MJ/m²/day using 1 W/m² = 0.0864 MJ/m²/day, which is convenient for daily energy accounting. Typical nighttime L↓ often falls near 250–400 W/m², while L↑ from warm surfaces can exceed 450 W/m².

3) Typical temperature ranges used in practice

Near-surface land temperatures commonly span 0–60 °C, while effective sky temperature can be several degrees lower at night under clear conditions. A 10 °C decrease in sky temperature can reduce L↓ substantially, increasing negative Rnl and accelerating surface cooling.

4) Emissivity values and surface types

Surface emissivity εs is often high: water and dense vegetation are typically 0.97–0.99, while dry soils may range about 0.90–0.97. Small emissivity changes matter because radiation scales with T⁴, so warm surfaces with slightly lower ε can still emit strongly.

5) Sky emissivity and atmospheric moisture

Clear-sky emissivity εsky is commonly around 0.70–0.90, depending on humidity and temperature. More water vapor increases atmospheric longwave emission, raising L↓. In the Brutsaert option, vapor pressure ea (often ~0.5–3.5 kPa near the surface) helps estimate εsky.

6) Cloud effects on longwave exchange

Clouds behave like efficient infrared emitters, so overcast conditions push εsky toward 1.0. That increases L↓ and reduces longwave cooling at the surface. The cloud fraction slider blends clear-sky ε with a near-blackbody sky, capturing this first-order behavior.

7) Interpreting positive and negative results

If Rnl is negative, the surface loses more longwave energy than it gains, which is typical at night for warm land under clear skies. If Rnl is closer to zero or positive, the atmosphere is supplying strong longwave back-radiation, common in humid or cloudy conditions.

8) Good measurement and modeling habits

Use consistent units and prefer Kelvin internally for radiation laws. When using direct flux mode, ensure your L↓ and L↑ come from comparable sensor geometry and time averaging. For modeling, treat Tsky as an effective parameter; calibrate ε values with local observations when accuracy is critical. If you use weather-station air temperature, expect biases on clear nights and over snow or dry air.

FAQs

1) What does net longwave radiation represent?

It is the difference between downward atmospheric longwave and upward surface longwave. The sign indicates whether the surface gains or loses longwave energy during the selected conditions.

2) Why do I need Kelvin for the calculation?

Stefan–Boltzmann uses absolute temperature, so the T⁴ term must use Kelvin. The calculator converts °C and °F to Kelvin automatically before computing flux.

3) What emissivity should I use for vegetation?

Vegetation usually has high emissivity, often around 0.97–0.99. If you lack site data, 0.98 is a common and reasonable starting value.

4) How do clouds change the result?

Clouds increase sky emissivity, boosting downward longwave radiation. This typically reduces night-time cooling and makes net longwave less negative compared with clear-sky conditions.

5) What is vapor pressure in the Brutsaert option?

Vapor pressure ea measures atmospheric moisture and is entered in kPa, hPa, or Pa. Higher ea generally increases estimated sky emissivity and L↓.

6) When should I use direct flux mode?

Use it when you already have measured or modeled L↓ and L↑. This mode simply computes net longwave by subtraction and provides the same export outputs.

7) How should I interpret MJ/m²/day values?

They express daily energy totals rather than instantaneous flux. Multiply W/m² by 0.0864 to get MJ/m²/day, which is helpful for daily surface energy balance summaries.

Related Calculators

Air Quality Index (AQI) CalculatorPM2.5 Concentration to AQI CalculatorPM10 Concentration to AQI CalculatorOzone (O3) AQI CalculatorNitrogen Dioxide (NO2) AQI CalculatorSulfur Dioxide (SO2) AQI CalculatorCarbon Monoxide (CO) AQI CalculatorVentilation Rate (ACH) CalculatorPollutant Mass Balance (Indoor) CalculatorDeposition Velocity Calculator

Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.