Fill Factor Calculator

The fill factor indicates how close a solar cell is to the theoretically optimal state. The value of a perfect cell is 1, i.e. 100%, where all available voltages and currents are converted into usable power. Typical actual values for silicon cells range from about 0.70 to 0.85.

Please enter the four numbers derived from the cell's I-V curve: open circuit voltage, short circuit current, voltage and current at maximum power point. The calculator will give you the fill factor as a percentage and can also be used to convert. If one of the input fields is left blank, that value will be calculated.

What is fill factor?

Imagine the I-V curve of a perfect solar cell. It would be a sharp rectangle. The current stays constant at Isc until the voltage reaches Voc, after which it falls linearly to zero. All the useful power is contained in the area of this rectangle, i.e., the product of Voc and Isc.

A real cell does not behave like this. As the voltage rises, the current falls and the curve becomes more rounded and forms a kink. The largest rectangle that fits under this actual curve has Vmp and Imp as its sides. These are the voltage and current of the point of maximum power. The fill factor is the ratio of this small rectangle to the ideal rectangle and serves as a measure of how close the curve comes to being rectangular.

Formula for fill factor:

The fill factor is the value obtained by dividing the actual maximum power by the product of the open-circuit voltage and short-circuit current.

Since both the numerator and denominator are power outputs in watts, the units cancel out, and the fill factor is a dimensionless number between 0 and 1. Multiplying by 100 gives a percentage value. Because the same relationship connects these five quantities, the formula can be rearranged to calculate any one of the other four values given the unknown quantity. The input fields are left blank for this reason.

To use this calculator:

Measure the four points on the cell under a constant illumination level and temperature then enter the values. The fill factor will be displayed as a major result along with a graph showing the maximum power, ideal power and how close the curve is to being rectangular.

If you want to work backwards, enter the fill factor and three of the four measurements and leave the unknown field blank. No mode selection is required. By simply leaving a field blank, you are telling the calculator which value it should calculate. The two checkboxes allow you to include cell efficiency as well as a comparison with the theoretical maximum fill factor.

Example calculation

Assume a single monocrystalline silicon cell is tested under standard conditions. The measured values are: Voc = 0.7V, Isc = 9.5A, Vmp = 0.58V, Imp = 9.0A.

The ideal power is 6.65W (the product of 0.7 and 9.5). The actual maximum power is 5.22W (the product of 0.58 and 9.0). If you divide both values:

Cell performance is about four-fifths of the theoretical maximum which is good for a commercial silicon panel, and the remaining 1.43W are losses due to the rounded knees in the curve.

Alternative formulations of the filling factor:

This table shows the same relationship in five different forms and assigns a value to each possible missing item.

Why is the fill factor not equal to 100%?

Two different types of internal resistances cause the actual cells to deviate from an ideal rectangle. The series resistance is present in the silicon material itself, the metal grid lines and contacts. A high series resistance "squeezes" the I-V curve sideways and reduces Vmp.

The parallel resistance has the opposite effect. It represents a loss of current through cell edges or material defects. A low parallel resistance will cause the curve to fall below the peak and reduce Imp below Isc.

If the calculated fill factor is less than 0.70 it is usually due to one of these two types of resistance. Good cells will normally have a measured value between 0.70 and 0.85, while values above 0.85 are mostly only found in high performance or research grade cells.

Theoretical maximum fill factor:

The fill factor has an upper limit which is determined by the cell's open circuit voltage alone. Cells with higher voltages can achieve a higher fill factor, because the rounded part of the curve makes up a smaller proportion of the rectangular area.

A widely used empirical formula allows to determine this upper limit for ideal cells without resistive losses. This formula uses the normalized voltage voc:

where n is the diode ideality factor, k is Boltzmann's constant, T is the absolute temperature and q is the elementary charge. If you turn on the switch for theoretical maximum then the calculator will calculate this limit based on Voc and show what percentage of that limit your actual cell achieves. The difference between these two values gives a direct measure of how much loss there is due to resistance.

Fill factor and efficiency

The fill factor describes the shape of the curve but does not represent all cell performance. The efficiency is the ratio of output power to input solar light and both are related by Voc and Isc:

Pin is the input power of light, i.e., the product of irradiance G and cell area A. Under standard test conditions, 1000 W/m² is used, which corresponds to full sunlight. When you enter the area and irradiance in the efficiency level, the calculation tool converts the maximum power into an efficiency. Increasing the fill factor, voltage or current leads to improved efficiency.

Why this is important for industry

When manufacturers announce new efficiency records, an improved fill factor is often one of the reasons. Thinner silver contacts, purer silicon and better contact passivation reduce resistance, raise the fill factor to 0.85, and allow more power to be extracted from the same area receiving light.

In the manufacturing of gigawatts, an improvement in the fill factor by one point leads to a corresponding increase in module power. This value is very important. For this reason, many cell construction works pay special attention to the resistance that results from the fill factor.

Tips for accurate results:

Measure all four values at the same illumination level and temperature. Use industry standard test conditions of 1000W/m2 irradiance, 25 degrees C and an AM1.5 spectrum.

Before accepting the calculation results, make sure Vmp is less than Voc and Imp is less than Isc. If this rule is violated, the calculator will show a warning. This is because the maximum power point always lies within a rectangle defined by Voc and Isc. Misreading points on the curve will lead to an overestimated fill factor.