Enter the global horizontal irradiance (GHI) and the solar zenith angle into the calculator to estimate the direct normal irradiance (often abbreviated DNI; sometimes called “direct normal radiation” on an irradiance basis) under the simplifying assumption that diffuse horizontal irradiance is negligible (DHI ≈ 0).

Direct Normal Irradiance (DNI) / Direct Normal Radiation (DNR) Calculator

Note: This calculator uses the approximation DNI ≈ GHI / cos(θ), which assumes diffuse horizontal irradiance (DHI) ≈ 0. In general, GHI = DNI · cos(θ) + DHI.

Enter any 2 values to calculate the missing variable (using the approximation above)

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Direct Normal Radiation Formula

The following approximation can be used to estimate direct normal irradiance (DNI) from global horizontal irradiance (GHI) and solar zenith angle when the diffuse horizontal irradiance is negligible (DHI ≈ 0). In general, the relationship is GHI = DNI · cos(θ) + DHI.

DNI ≈ GHI / cos(θ)

Variables:

  • DNI (sometimes labeled DNR) is the direct normal irradiance (power per unit area), typically in W/m²
  • GHI is the global horizontal irradiance on a horizontal surface (W/m²), which equals DNI · cos(θ) only if DHI ≈ 0
  • θ is the solar zenith angle (the calculator accepts degrees or radians)

To estimate DNI from GHI using this approximation, divide the (beam-only) horizontal irradiance by the cosine of the solar zenith angle. If you know the diffuse horizontal irradiance (DHI), a more general estimate is DNI = (GHI − DHI) / cos(θ) (when cos(θ) ≠ 0).

What is Direct Normal Radiation?

Direct Normal Irradiance (DNI)—sometimes informally called direct normal radiation when expressed as irradiance—is the solar irradiance (power per unit area, e.g., W/m²) coming directly from the sun’s disk, measured on a surface held perpendicular (normal) to the sun’s rays. It is widely used in solar resource assessment and is especially important for concentrating solar power systems and for separating the direct-beam component from diffuse light in solar energy modeling.

How to Calculate Direct Normal Radiation?

The following steps outline how to estimate the Direct Normal Irradiance using the approximation on this page (assumes DHI ≈ 0).

  1. First, determine the global horizontal irradiance (GHI).
  2. Next, determine the solar zenith angle (θ).
  3. Next, calculate the cosine of the solar zenith angle.
  4. Finally, estimate the direct normal irradiance using the approximation DNI ≈ GHI / cos(θ).
  5. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Global Horizontal Irradiance (GHI) = 800 W/m²

Solar Zenith Angle (θ) = 30 degrees. Using the approximation (DHI ≈ 0), DNI ≈ 800 / cos(30°) ≈ 923.7604 W/m².