P50 vs P90 in Solar: Meaning, Formula and Worked Example

P50 is the yearly energy yield that a PV (solar panel) plant has a 50% chance of exceeding. P90 is the yield it has a 90% chance of exceeding, so it is lower. On a normal distribution (a bell curve), P90 sits about 1.28 standard deviations below P50. P90 is not 90% of P50. It is also not a guarantee for any single year.

What does P50 mean?

P50 is the median of the modeled yearly yield. The median is the middle value. Half of the modeled years come out above it and half below.

PVsyst’s P50–P90 documentation defines P50 and P90 as exceedance values. PVsyst is photovoltaic simulation software. Its documentation says yearly production has a 50% probability of exceeding P50 and a 90% probability of exceeding P90. Always state the energy units and the time horizon next to the probability. Without them, you cannot compare the number with anything.

What does P90 mean?

P90 is the 10th percentile of the same distribution. Only 10% of modeled years fall below it. The model puts 90% of the probability above it.

For a normal distribution, PVsyst’s documentation puts P90 1.28 standard deviations (σ) below the mean. A standard deviation shows how widely results spread around the average. The mean is that average. For a symmetric normal curve, the mean equals P50.

Other exceedance values work the same way. P75 is exceeded with 75% probability, so it sits between P50 and P90. P99 is exceeded with 99% probability and sits far below both. PVsyst’s tool lets you ask for P90 “or other values”.

P90 is not 90% of expected production

“P90” is a label for the chance of exceeding the value. It does not cut the energy by a fixed percentage. Two projects can have the same P50 and different P90 estimates, because their modeled uncertainty differs.

A smaller gap between P50 and P90 does not prove that one model is more accurate. The gap may come from better evidence, different assumptions, or uncertainty that the model left out. Read the inputs before you use the ratio to compare projects.

The P90 formula and a worked example

When the chosen model is normal and its mean equals P50, the lower percentile is:

P90 = P50 − 1.2816 × σ
P90 = P50 × (1 − 1.2816 × σ%)     (σ% = σ as a fraction of P50)

σ is the standard deviation, in the same energy units as P50. If σ is given as a percentage, convert it to energy before you subtract it. The multipliers for P75 and P99 are 0.6745 and 2.3263. These are the standard normal values for the 25th and 1st percentiles (see the NIST standard normal table for the same distribution).

Assume P50 is 10,000 MWh/year. The three σ values below are example inputs. They are not a measured plant or a SurgePV benchmark.

For the 5% row: P90 = 10,000 − 1.2816 × 500 = 10,000 − 640.8 = 9,359.2, rounded to 9,359 MWh/year. P75 = 10,000 − 0.6745 × 500 = 9,662.75. P99 = 10,000 − 2.3263 × 500 = 8,836.85.

You cannot get a project’s P90 from a fixed discount off P50. The same P50 gives a P90 of 9,359 MWh/year at 5% σ and 8,718 MWh/year at 10% σ. The discount comes from the project’s own uncertainty.

Where σ comes from

According to the PVsyst documentation, the biggest part of σ is the uncertainty and year-to-year change in the weather data. Its interannual-variability page says yearly irradiation (sunlight energy) over a long record is well matched by a normal distribution. A long record is typically 10 to 30 years. The page gives a default variability of 5.1% at 900 kWh/m² and 3.5% at 1,700 kWh/m².

It also says typical values can differ a lot from that model, so compute the variability for your site. Other parts add on top. After weather, the PV module model is the main one. Soiling (dirt on the panels) and module quality loss depend heavily on site conditions.

Normal distribution or measured distribution?

The formula above assumes a normal distribution. It is one method, not the only one. The NREL (National Renewable Energy Laboratory) paper P50/P90 Analysis for Solar Energy Systems Using the System Advisor Model (Dobos, Gilman and Kasberg, 2012) describes two. One fits a normal distribution to the yearly results. The other reads the P-value straight from the measured spread of the data (the empirical distribution), with no set distribution assumed.

For the three PV systems it simulated in Phoenix, the normal-distribution method gave a P90 “a few percent more optimistic” than the empirical method. State which method a report used.

What belongs in the uncertainty assessment?

In PVsyst’s model, every uncertainty source is treated as random. The sources are added in quadrature to give one σ. Adding in quadrature means squaring each one, adding the squares and taking the square root.

The sources should represent random year-to-year variability, not absolute uncertainty. PVsyst lists long-term degradation as not compatible with the P90 concept. Record where each input came from. Note whether it covers weather variation, measurement uncertainty or model uncertainty.

Use this review table to make the evidence easy to check:

Adding components in quadrature assumes they are independent. If two components move together, the combined σ comes out too low. Write down the assumption for each pair that does.

PVsyst also says a P90 is only meaningful for yearly yields. Yearly irradiation varies typically 3 to 4% (RMS, the root-mean-square spread) from year to year. Individual months vary much more. A reliable P90 needs a long record, at least 15 to 20 years.

Some people build a “P90 time series” by scaling every hourly result by the P90/P50 ratio. This is incorrect, because a clear-sky hour produces the same output in any scenario. The gap between a P50 year and a P90 year comes from how often and how badly the weather turns poor.

Single-year and multiyear P90 are different questions

A single-year value covers the modeled energy for one year. A multiyear average covers the average across a stated period. Do not compare them until the time horizon and the uncertainty treatment match.

Dividing all uncertainty by the square root of the number of years is wrong as a general shortcut. Only the independent random part shrinks that way. A systematic bias (a steady error in one direction) or a linked component does not average out over more years. The report should say which components it reduced, which it kept, and why.

P50 vs P90 for cost estimates

The same labels are used for project costs, and the direction flips. A P90 cost is the cost that outcomes stay at or below in 90% of cases, so it is higher than the P50 cost. A P90 energy yield is lower than the P50 yield. These are two separate distributions. A financial model should carry them as separate scenarios. The P50 vs P90 cost estimates guide covers the cost side, including how contingency (extra budget set aside for risk) is built.

How to compare two energy-yield reports

First, line up the project boundary. Are both reports estimating DC generation, inverter AC output, or electricity delivered at the revenue meter? DC is the direct current the panels make. AC is the alternating current after the inverter. Then line up weather data, layout, equipment, loss assumptions, degradation treatment and time horizon.

Compare the P-values only after those inputs match. If a report gives a P90 without its uncertainty basis, ask for the method. A P90 with no stated basis is not independent evidence of quality.

SurgePV and PVsyst are products from different companies. This guide cites PVsyst’s public documentation for the method. SurgePV publishes this guide and sells yield-modeling software.

The solar simulation workflow and the energy simulation guide show how SurgePV organizes model inputs and outputs. The solar yield prediction guide covers weather data, losses and validation in more depth.

Using P-values in financial evaluation

Use the energy scenario that the lender, investor or contract asks for, with its assumptions. A cautious energy estimate alone does not prove enough revenue. Price, curtailment (output cut back by the grid or buyer), availability (how often the plant is running), operating costs and debt terms also matter.

Keep the energy assessment and the financial model connected through written scenarios. Each lender or investor decides what it accepts. No P90/P50 ratio proves on its own that a project can get financing. The solar lender engineer guide explains what an independent engineer reviews in a yield report.

Frequently asked questions

What does P50 mean in solar?

P50 is the yearly energy yield that a PV plant has a 50% chance of exceeding. It is the median (middle value) of the modeled yield, so half of the modeled years come out above it and half below.

What is the difference between P50 and P90?

P50 is exceeded 50% of the time and P90 is exceeded 90% of the time, so P90 is the lower number. How far below depends on the uncertainty (sigma) in the model. On a normal distribution, P90 is about 1.28 standard deviations below P50.

Is P90 always 90% of P50?

No. P90 is the yield you have a 90% chance of exceeding. How it compares with P50 depends on the distribution, the uncertainty assumptions and the time horizon. With a standard deviation of 5% of P50, P90 is about 93.6% of P50. At 10% it is about 87.2%.

Does a P90 estimate guarantee production in nine of the next ten years?

No. It is a statement of probability under a model. It is not a promise about any particular run of future years.

What must accompany a P90 number?

Record the energy units, project boundary, time horizon, weather and equipment assumptions, uncertainty components and calculation method.

Can P50 and P90 be used for cost estimates?

Yes, but the direction flips. A P90 cost is higher than the P50 cost, while a P90 energy yield is lower than the P50 yield. Keep the two distributions separate in a financial model.