Clearness Index (Kt): Formula From GHI for PV

Last updated: November 2026

Two sites at the same latitude can produce very different solar yields, and one number explains much of the gap. The solar clearness index (Kt) measures how much of the sunlight above the atmosphere actually reaches the ground. The difference is not sun angle. It is clouds, aerosols, water vapor, and atmospheric clarity.

Kt sits upstream of every major PV design decision. It controls how global horizontal irradiance (GHI) decomposes into direct and diffuse light. It shapes the optimal tilt. It affects whether a tracking system pays off. And it feeds the kWh/kWp predictions that drive project finance.

This 2026 guide explains what the clearness index measures, how to calculate it, and what values to expect by climate. It also shows how to avoid the mistakes that silently corrupt yield models.

What you will learn:

• The exact definition of solar clearness index and its formula
• How to calculate Kt from GHI and extraterrestrial irradiance
• Typical Kt ranges by climate, season, and sky condition
• Why Kt controls GHI decomposition and PV yield predictions
• The difference between clearness index and clear-sky index
• Common modeling mistakes and how to avoid them
• Where Kt fits in a yield workflow, and how to check it

Solar Clearness Index 2026: Definition and Formula

The solar clearness index is a dimensionless ratio. It compares the solar radiation measured on a horizontal surface at ground level to the radiation that would strike the same horizontal surface above the atmosphere. The concept goes back to Liu and Jordan in 1960 and remains a foundation of solar resource analysis.

The formula is simple:

Kt = GHI / EHI

Where:

• Kt = clearness index (unitless)
• GHI = global horizontal irradiance at ground level (W/m² or kWh/m²)
• EHI = extraterrestrial horizontal irradiance (same units)

GHI is the total sunlight on a flat horizontal surface. It includes direct beam radiation, diffuse sky radiation, and reflected ground light. EHI is the sunlight available on the same horizontal plane but outside Earth’s atmosphere. It depends only on the solar constant, the Earth-Sun distance, and the solar elevation angle.

Because EHI removes the geometry of the sun’s position, Kt isolates the atmospheric effect. Two sites at very different latitudes can have the same Kt on the same day, even though their absolute GHI values differ sharply. A site at high latitude in summer might receive 400 W/m² of GHI. A desert site at noon might receive 950 W/m². If both have Kt = 0.70, their atmospheres are equally clear.

Extraterrestrial Irradiance: The Denominator

The denominator in the clearness index is not constant. It varies through the year because Earth’s orbit is elliptical. The Earth is closest to the sun in early January and farthest in early July. That distance change produces about a 3.3% swing in extraterrestrial irradiance.

The extraterrestrial normal irradiance (ENI) is:

ENI = Esc × (1 + 0.033 × cos(theta))

Where:

• Esc = solar constant = 1,361 W/m², as adopted by PVsyst from version 8.1 (PVsyst documents it as correcting calibration errors in earlier measurements; versions before 8.1 used 1,367 W/m²)
• theta = orbital angle of the Earth around the sun, measured from January 1

To get EHI on a horizontal plane, project ENI by the sine of the solar altitude angle (HSol):

EHI = ENI × sin(HSol)

At solar noon on the equator, HSol can reach 90° and sin(HSol) = 1. At 40°N latitude in winter, HSol might only reach 26°, so sin(HSol) ≈ 0.44. The same clear atmosphere produces a much lower EHI at high latitudes in winter, even though Kt stays the same.

Why Kt Is Not the Same as Solar Efficiency

A common confusion treats Kt like an efficiency percentage. It is not. Kt does not tell you what share of sunlight the atmosphere converts to useful energy. It tells you what share of extraterrestrial radiation reaches the ground as GHI. The atmosphere scatters and absorbs some light. The ground receives the rest as GHI, which itself still contains wavelengths that PV modules cannot use efficiently.

A Kt of 0.65 does not mean 65% efficiency. It means the ground receives 65% of the extraterrestrial horizontal irradiance. The PV system then converts only a fraction of that GHI into electricity, after module efficiency and losses for temperature, soiling, mismatch, and the inverter.

How to Calculate Clearness Index Step by Step

Most solar designers never calculate Kt manually. Simulation software computes it from imported GHI data. Understanding the steps helps you spot errors and interpret validation warnings.

Step 1: Obtain GHI for the Same Time Step

Use GHI measured or modeled at the time step you need. Hourly Kt requires hourly GHI. Daily Kt requires daily GHI. Mixing time steps produces meaningless results. If your pyranometer records irradiance in W/m², convert it to irradiation in kWh/m² by multiplying by the time interval in hours.

For example, a steady 600 W/m² for one hour equals 0.600 kWh/m².

Step 2: Calculate the Solar Position

You need the solar declination, hour angle, and zenith or altitude angle for the location and time. These come from standard solar position equations based on latitude, longitude, date, and local solar time. Most tools use a solar position library such as pvlib or the NREL solar position algorithm.

Step 3: Compute EHI

First find ENI using the orbital distance correction. Then project it onto the horizontal plane:

EHI = 1,361 × (1 + 0.033 × cos(theta)) × sin(HSol)

At sunrise and sunset, HSol approaches 0°, so EHI approaches 0. That makes Kt unstable near the horizon. PVsyst handles this by setting Kt = 0 when HSol drops below 2°, as noted in the PVsyst clearness index documentation.

Step 4: Divide GHI by EHI

Kt = GHI / EHI

The result is unitless. For instantaneous values, Kt can swing rapidly as clouds pass. For monthly averages, values are stable and comparable across years.

Worked Example: Phoenix, 21 June, Solar Noon

The GHI value below is an illustrative input, not a measurement. The geometry is real.

Inputs:

• Latitude: 33.45°N
• Date: 21 June (day 172)
• Solar noon altitude (HSol): 79.8°
• GHI at solar noon (illustrative input): 1,015 W/m²

Orbital angle:

theta = (172 - 1) × (360 / 365) = 168.7°

ENI:

ENI = 1,361 × (1 + 0.033 × cos(168.7°)) ENI = 1,361 × (1 + 0.033 × (-0.982)) ENI = 1,361 × 0.968 = 1,317 W/m²

EHI:

EHI = 1,317 × sin(79.8°) EHI = 1,317 × 0.984 = 1,296 W/m²

Kt:

Kt = 1,015 / 1,296 = 0.78

A Kt of 0.78 indicates a very clear sky. Hazier or partly cloudy conditions at the same geometry give a lower GHI, so a lower Kt, a larger diffuse share and a different plane-of-array irradiance.

Typical Clearness Index Values and Documented Limits

Kt follows climate. Cloud cover is the dominant driver, aerosols from deserts, wildfires or urban pollution also matter, and altitude helps because the atmosphere is thinner. Published tables of Kt by city vary with the dataset and the year, so this guide does not give a city-by-city table. Pull monthly Kt from the dataset you will use for the project instead.

What the software documentation does state clearly are the limits below.

Sources: the PVsyst clearness index documentation and the pvlib clearness_index documentation, checked November 2026.

Instantaneous Kt moves much more than monthly Kt. A clear sky gives a high value, thick overcast gives a very low one, and short cloud-enhancement events can push it above 1. There are no standard cut-offs between sky classes, because thresholds differ by model and application.

Seasonal Variation Matters More Than Annual Average

Annual average Kt is a useful headline number and a misleading one for project finance. A site with a respectable annual average can still have a very low winter Kt. That seasonal shape affects:

• Battery sizing: Low winter Kt means longer cloudy spells and deeper discharge cycles.
• Load matching: High summer Kt may coincide with air-conditioning loads in hot climates.
• Revenue modeling: Time-of-use rates may reward summer afternoon production more than annual kWh.

Always review monthly Kt, not just the annual number. Most design tools show this in the meteo summary. If yours does not, compute it from monthly GHI and EHI.

Where to Get GHI Data

Most designers do not measure Kt directly. They pull GHI from satellite databases such as PVGIS, Meteonorm, or Solargis, and the software computes Kt. Ground stations in the BSRN network let you calculate Kt from measured GHI. For bankable projects, cross-check at least two sources.

Why Clearness Index Drives PV Yield Accuracy

Kt matters because it is the gateway to GHI decomposition. Most irradiance databases give you GHI. Your simulation needs to split that GHI into direct and diffuse components before it can transpose them onto a tilted array.

From Kt to Diffuse Fraction

The diffuse fraction (kd) is the share of GHI that arrives as diffuse radiation. Empirical models estimate kd from Kt. The relationship is inverse: as Kt rises, the diffuse fraction falls. Clear skies produce mostly direct beam. Cloudy skies produce mostly diffuse light.

The classic Erbs model is an empirical correlation between Kt and diffuse fraction published by Erbs, Klein and Duffie in 1982 (implemented in pvlib). The Orgill and Hollands model does the same for hourly data. The Boland-Ridley-Lauret (BRL) model uses a logistic function that handles the transition between clear and cloudy conditions more smoothly.

None of these correlations is universal. They vary by climate, season, and aerosol load. That is why bankable projects often use measured DNI and DHI from high-quality datasets rather than deriving them from GHI alone.

Impact on Plane-of-Array Irradiance

Once GHI is split into DNI and DHI, the software transposes each component onto the array plane. The direct beam gains from tilt and tracking. The diffuse component depends on sky anisotropy and ground reflection. The total is plane-of-array irradiance (POA).

Once GHI is split into DNI and DHI, the software transposes each component onto the array plane. The direct beam gains from tilt and tracking. The diffuse component depends on sky anisotropy and ground reflection. The total is plane-of-array irradiance (POA).

An error in Kt changes the split, so it changes POA, the energy yield, the performance ratio, and the project IRR. On a large system the revenue impact of a small systematic bias compounds over the project life. For how the uncertainty is reported, see the P50 and P90 energy yield guide.

Impact on Technology Choice

High-Kt climates favor technologies that capture direct beam efficiently. Single-axis trackers provide large gains because they keep the direct beam perpendicular to the module. Bifacial modules benefit from high ground-reflected albedo in dry, high-Kt locations.

Low-Kt climates shift the economics toward fixed-tilt systems with good diffuse capture, because overcast skies reduce the value of tracking.

Clearness Index vs. Clear-Sky Index

These two terms sound similar but measure different things. Confusing them leads to bad forecasts and misinterpreted performance data.

Clearness Index (Kt)

Kt compares actual GHI to extraterrestrial irradiance. It removes the predictable annual geometry trend but keeps the atmosphere’s clear-sky attenuation. You use Kt for:

• Decomposition models
• Long-term resource assessment
• Comparing atmospheric clarity across sites and seasons

Clear-Sky Index (Kc or k*)

The clear-sky index compares actual GHI to a modeled clear-sky GHI for the same location and time. The clear-sky model accounts for solar geometry, aerosols, water vapor, and ozone. The clear-sky index therefore isolates cloud variability. You use it for:

• Solar forecasting
• Nowcasting
• Detecting cloud enhancement events

Why the Distinction Matters

A desert site might have Kt = 0.75 and clear-sky index = 1.0 on a clear day. Both values say the sky is clear. A humid tropical site might have Kt = 0.55 but clear-sky index = 1.0 on a clear day. The low Kt comes from persistent water vapor and aerosol absorption, not clouds. The clear-sky index reveals that distinction.

If you use Kt to forecast clouds, you will misinterpret high-humidity clear days as partly cloudy. If you use the clear-sky index for long-term resource mapping, you need a reliable clear-sky model everywhere you work.

Common Mistakes Designers Make

Even experienced designers mishandle clearness index. Here are the most common errors and how to avoid them.

Mistake 1: Confusing Annual and Instantaneous Kt

Annual average Kt cannot tell you what happens on a partly cloudy afternoon. Hourly Kt can spike above 1 during cloud enhancement or fall sharply under thick cloud. Use annual averages for resource mapping and climate comparison. Use sub-hourly or hourly values for yield modeling and forecasting.

Mistake 2: Ignoring the Solar Constant Update

Older references use 1,367 W/m² for the solar constant. PVsyst 8.1 and later use 1,361 W/m². A 0.4% difference seems small, but it changes the absolute Kt and can trigger validation warnings when you import old data into new software.

Mistake 3: Using the Wrong Time Step

You cannot divide monthly GHI by hourly EHI. The numerator and denominator must cover the same integration period. Daily Kt needs daily GHI and daily EHI. Hourly Kt needs hourly values. Mixing steps produces nonsense ratios.

Mistake 4: Treating Kt as a Fixed Site Constant

Kt varies by season, year, and even hour. A site does not have “a” clearness index. It has a distribution of Kt values. P50/P90 yield analysis depends on that distribution, not on a single average.

Mistake 5: Forgetting the Low-Sun Cutoff

Near sunrise and sunset, EHI approaches zero. Small measurement errors in GHI create huge swings in calculated Kt. Quality tools apply a cutoff at low solar elevations: PVsyst sets Kt to 0 below 2° solar height, and pvlib uses a minimum cos(zenith) of 0.065. If you calculate Kt manually, pick a cutoff and document it.

Mistake 6: Overlooking Cloud Enhancement

Measured GHI can exceed EHI for short periods when clouds reflect or focus sunlight. This produces Kt > 1. Some older decomposition models cannot handle these events and may crash or give invalid diffuse fractions. pvlib caps the maximum clearness index at 2.0 by default to allow for sub-hourly over-irradiance, as documented in the pvlib clearness_index function.

Where Clearness Index Fits in a Design Workflow

Tracking Kt by hand for every project is not practical. Kt is computed inside the yield model from the weather file you import. What you control is the quality of that input and whether you check it.

SurgePV is solar design software that supports energy-yield modeling, shading analysis and financial modeling in one workflow, so the weather data, shading and financial model sit in one project. As with any yield tool, results depend on source data, assumptions, equipment models and configuration, and need engineering review. Related reading: DNI and DHI explain the components that Kt helps estimate, and performance ratio shows how yield is judged against the resource.

For quick checks, the solar panel sizer, solar power calculator and ROI payback calculator are free tools on this site.

Conclusion

The solar clearness index is a small ratio with an outsized impact. It distills clouds, aerosols, water vapor, and atmospheric clarity into a single number that feeds every downstream PV calculation. Get Kt right, and your yield model starts from a solid foundation. Get it wrong, and the error multiplies through decomposition, transposition, and financial forecasting.

Three actions to take from this guide:

1. Check the implied Kt in your next simulation. Compare monthly values to the 0.12 to 0.82 range PVsyst documents. Values outside it should trigger a data review.

2. Use measured or high-quality modeled DNI and DHI when possible. Decomposition models work, but direct inputs reduce uncertainty. Cross-check two data sources for commercial projects.

3. Distinguish Kt from the clear-sky index. Use Kt for resource assessment and decomposition. Use the clear-sky index for forecasting and cloud detection. Mixing them leads to wrong conclusions.

To check your own yield inputs against a worked model, book a SurgePV demo and bring a live project.

Frequently Asked Questions

What is the solar clearness index?

The solar clearness index (Kt) is the ratio of global horizontal irradiance (GHI) at ground level to the extraterrestrial irradiance on a horizontal plane above the atmosphere. It measures how much the atmosphere attenuates sunlight. PVsyst documents monthly averages usually falling between about 0.12 and 0.82, and instantaneous values can briefly exceed 1 during cloud enhancement.

How do you calculate clearness index?

Divide measured GHI by extraterrestrial horizontal irradiance (EHI). EHI equals extraterrestrial normal irradiance (ENI) times the sine of the solar altitude, and ENI = 1,361 x (1 + 0.033 x cos(theta)), where theta is the Earth’s orbital angle measured from January 1. Use the same time step for both: hourly Kt from hourly GHI, daily Kt from daily GHI.

What is a good clearness index for solar?

A higher Kt means a clearer atmosphere and more direct beam, but there is no universal good value. What matters is the monthly pattern at the site, not one annual average. PVsyst expects monthly averages between about 0.12 and 0.82, so values outside that range usually point to a data problem.

What is the difference between clearness index and clear-sky index?

Clearness index compares actual GHI to extraterrestrial irradiance, so it removes solar geometry but keeps the effect of a clear atmosphere. Clear-sky index compares actual GHI to a modeled clear-sky GHI for the same place and time, which isolates cloud variability. Use Kt for decomposition and resource work, and the clear-sky index for forecasting.

Why does clearness index matter for PV design?

Clearness index drives how GHI is split into direct and diffuse components. That split feeds the transposition to the tilted array, so it affects the value of tracking, the plane-of-array irradiance and the predicted kWh/kWp. An error in Kt carries through to yield and financial estimates.

Can clearness index be greater than 1?

Yes, briefly. Clouds can act as lenses and raise measured GHI above extraterrestrial horizontal irradiance, which gives Kt above 1 in short time steps. PVsyst flags such values in imported data, and pvlib caps the clearness index at 2.0 by default.

How does PVsyst use clearness index?

PVsyst defines Kt as GHI divided by extraterrestrial horizontal irradiance, using a solar constant of 1,361 W/m2 from version 8.1 (1,367 W/m2 before). It expects monthly averages between about 0.12 and 0.82, and it sets Kt to 0 when the solar height is below 2 degrees. Those limits can be changed in advanced parameters.