Calculate direct normal irradiance (DNI), global horizontal irradiance, or solar zenith angle from two values using DNI≈GHI/cos(θ).

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)

Related Calculators

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

The calculator uses the beam-only approximation for solar irradiance on a horizontal surface. It assumes diffuse horizontal irradiance is approximately zero, so GHI is treated as the horizontal component of DNI.

DNI ≈ (GHI) / (cos(θ))
GHI ≈ DNI × cos(θ)
θ = ((GHI) / (DNI))

The more complete irradiance relationship is:

GHI = DNI × cos(θ) + DHI
  • DNI = direct normal irradiance, also called direct normal radiation in some contexts
  • GHI = global horizontal irradiance
  • DHI = diffuse horizontal irradiance
  • θ = solar zenith angle, measured from directly overhead
  • cos(θ) = cosine of the solar zenith angle

If you leave DNI/DNR blank, the calculator divides GHI by cos(θ). If you leave GHI blank, it multiplies DNI by cos(θ). If you leave the solar zenith angle blank, it uses arccos(GHI / DNI). Radiation values are converted internally to W/m², and angles are converted internally to degrees before the calculation.

Solar Zenith Angle and Cosine Reference

The cosine of the solar zenith angle controls how much direct normal irradiance projects onto a horizontal surface. As the sun gets lower in the sky, cos(θ) gets smaller and the same DNI produces less GHI.

Solar zenith angle cos(θ) Approximate GHI if DNI = 1000 W/m²
0° 1.000 1000 W/m²
30° 0.866 866 W/m²
45° 0.707 707 W/m²
60° 0.500 500 W/m²
80° 0.174 174 W/m²

Irradiance Unit Conversions

Conversion Factor
W/ft² to W/m² multiply by 10.7639
W/m² to W/ft² divide by 10.7639
radians to degrees multiply by 180 / π
degrees to radians multiply by π / 180

Example Calculations

Example 1: Calculate DNI from GHI and solar zenith angle

Suppose GHI is 600 W/m² and the solar zenith angle is 60°.

DNI ≈ (600) / (cos(60⁾)
DNI ≈ (600) / (0.5) = 1200 W / m²

The estimated DNI is 1200 W/m², assuming DHI is approximately zero.

Example 2: Calculate solar zenith angle from GHI and DNI

Suppose GHI is 707 W/m² and DNI is 1000 W/m².

θ = ((707) / (1000))
θ = (0.707) ≈ 45^

The estimated solar zenith angle is about 45°.

FAQ

What is the difference between DNI, DNR, GHI, and DHI?

DNI is direct normal irradiance, measured on a surface kept perpendicular to the sun’s rays. DNR is often used to mean direct normal radiation and is commonly treated the same way in this type of calculation. GHI is global horizontal irradiance, measured on a flat horizontal surface. DHI is diffuse horizontal irradiance, which is sunlight scattered by the atmosphere and received on a horizontal surface.

Why does this calculator assume DHI is approximately zero?

The calculator uses the simplified relationship DNI ≈ GHI / cos(θ). That only works when the diffuse part of horizontal irradiance is small enough to ignore. In real sky conditions, especially cloudy, hazy, or partly cloudy conditions, DHI can be significant. In those cases, the more complete formula is GHI = DNI · cos(θ) + DHI.

Why can the calculation fail near a 90° solar zenith angle?

At a 90° solar zenith angle, the sun is on the horizon and cos(θ) equals zero. Since the DNI formula divides by cos(θ), the result is undefined at that angle. Near 90°, small measurement errors can also create very large DNI estimates, so results close to the horizon should be treated carefully.