Find P80 Calculator

P80 Size Calculator

Enter two data points from your sieve analysis that bracket 80% passing to estimate the P80 size using linear interpolation.

Chart: Linear interpolation of P80 between two data points.

What is P80?

The P80 value represents the particle size at which 80% of the material, by mass or weight, is finer (smaller) than that size. It’s a common metric used in fields like mineral processing, powder metallurgy, and pharmaceuticals to characterize the fineness of a particulate material after processes like crushing, grinding, or screening. For example, if a sample of ground ore has a P80 of 150 microns, it means 80% of the ore particles are smaller than 150 microns.

This P80 calculator helps estimate the P80 size based on two known points from a particle size distribution curve, typically obtained from sieve analysis. Understanding the P80 is crucial for optimizing grinding circuits, predicting liberation size, and controlling the quality of the final product. The P80 calculator is particularly useful for engineers and technicians working with particulate materials.

Who should use it? Mineral processing engineers, metallurgists, lab technicians, and anyone dealing with particle size analysis will find the P80 calculator helpful. Common misconceptions include thinking P80 is the average size (it’s not, it’s a point on the distribution) or that it’s universally applicable without considering the material type.

P80 Formula and Mathematical Explanation

When you have two points from a sieve analysis that bracket the 80% passing mark, you can estimate the P80 using linear interpolation. Let’s say you have:

• (d1, P1): Sieve size 1 (d1) and the cumulative percent passing (P1), where P1 < 80%.
• (d2, P2): Sieve size 2 (d2) and the cumulative percent passing (P2), where P2 > 80%, and d2 > d1.

The formula for linear interpolation to find the size (d) corresponding to 80% passing (P80) is:

P80 = d1 + (80 – P1) * (d2 – d1) / (P2 – P1)

This assumes a straight line between the points (d1, P1) and (d2, P2) on a size vs. % passing graph. While particle size distributions are often not perfectly linear, this gives a reasonable estimate, especially when d1 and d2 are relatively close and bracket 80% tightly.

Variables Table

Variables used in the P80 calculation.

Variable	Meaning	Unit	Typical Range
P80	The particle size at which 80% of the material passes	microns, mm	1 – 500,000 microns
d1	Size of the smaller sieve opening bracketing P80	microns, mm	1 – 500,000 microns
P1	Cumulative percent passing through sieve d1	%	0 – 79.9
d2	Size of the larger sieve opening bracketing P80	microns, mm	d1 – 500,000 microns
P2	Cumulative percent passing through sieve d2	%	80.1 – 100

Using a P80 calculator simplifies this process.

Practical Examples (Real-World Use Cases)

Let’s see how the P80 calculator works with some examples.

Example 1: Grinding Circuit Output

A mineral processing plant grinds ore before flotation. Sieve analysis of the cyclone overflow shows:

• 106 microns: 75% passing (d1=106, P1=75)
• 150 microns: 88% passing (d2=150, P2=88)

Using the P80 calculator or the formula:

P80 = 106 + (80 – 75) * (150 – 106) / (88 – 75)

P80 = 106 + 5 * 44 / 13

P80 = 106 + 220 / 13 ≈ 106 + 16.92 ≈ 122.92 microns

The estimated P80 is about 123 microns. The plant operator can use this to adjust the grinding circuit if the target P80 is different.

Example 2: Powdered Material Specification

A company produces a powdered chemical and needs to ensure its P80 is below 75 microns. Lab results show:

• 63 microns: 78% passing (d1=63, P1=78)
• 90 microns: 85% passing (d2=90, P2=85)

Using the P80 calculator:

P80 = 63 + (80 – 78) * (90 – 63) / (85 – 78)

P80 = 63 + 2 * 27 / 7

P80 = 63 + 54 / 7 ≈ 63 + 7.71 ≈ 70.71 microns

The estimated P80 is about 71 microns, which meets the specification of being below 75 microns. You can use our P80 calculator above to verify.

How to Use This P80 Calculator

1. Enter Sieve Size 1 (d1): Input the size (e.g., in microns) of the sieve through which less than 80% of the material passed.
2. Enter Percent Passing 1 (P1): Input the percentage of material that passed through Sieve 1. This value must be less than 80.
3. Enter Sieve Size 2 (d2): Input the size (e.g., in microns) of the next larger sieve through which more than 80% of the material passed. d2 must be greater than d1.
4. Enter Percent Passing 2 (P2): Input the percentage of material that passed through Sieve 2. This value must be greater than 80.
5. Calculate: Click “Calculate P80”. The calculator will instantly display the estimated P80 size based on linear interpolation.
6. Read Results: The primary result is the calculated P80 size. Intermediate values show your input points. The chart visualizes the interpolation.
7. Reset: Click “Reset” to clear inputs to default values.
8. Copy: Click “Copy Results” to copy the P80 value and input data.

The P80 calculator provides a quick estimate. For more accurate results, especially if the distribution is highly non-linear between the two points, consider log-linear interpolation or fitting a distribution model (like Rosin-Rammler or Gates-Gaudin-Schuhmann) if more data points are available. Our particle size distribution calculator might be helpful.

Key Factors That Affect P80 Results

The P80 value is influenced by several factors, particularly in grinding and classification circuits:

• Feed Size (F80): The size distribution of the material fed into a grinding mill significantly affects the product P80. A finer feed generally leads to a finer product P80 for the same energy input.
• Grinding Media: The size, shape, material, and charge volume of grinding media (balls or rods) in a mill influence grinding efficiency and thus the P80.
• Mill Speed and Power: The operational speed of the mill and the power drawn affect the energy imparted to the material, influencing the final P80.
• Material Hardness and Toughness: Harder, tougher materials require more energy to break, making it harder to achieve a fine P80. The Bond Work Index is related to this.
• Classifier Efficiency: In closed-circuit grinding, the efficiency of the classifier (e.g., cyclone or screen) in separating fine and coarse particles directly impacts the P80 of the final product.
• Pulp Density/Viscosity: In wet grinding, the percentage of solids and the resulting pulp viscosity can affect grinding and classification efficiency, thus influencing P80.
• Sieve Analysis Accuracy: The reliability of the P80 value depends on the accuracy of the sieve analysis performed, including proper sampling and sieving technique. Using a reliable P80 calculator with accurate data is key.

Frequently Asked Questions (FAQ)

What does P80 mean?

P80 is the mesh size or particle diameter (in microns or mm) at which 80% of the particles by weight are smaller than that size, and 20% are larger.

Why is P80 important in mineral processing?

P80 is crucial for determining the efficiency of grinding circuits and the degree of liberation of valuable minerals from the ore. It affects downstream processes like flotation.

Is this P80 calculator accurate?

This calculator uses linear interpolation, which is an approximation. The accuracy depends on how close the two input data points are to the 80% mark and the actual shape of the particle size distribution curve between those points. For more precision, more data points and non-linear interpolation or curve fitting are needed.

What if my data points don’t bracket 80%?

This specific P80 calculator requires one point below 80% passing and one above. If you have data further away, the linear interpolation might be less accurate, or you might need more data points to estimate P80 reliably.

Can I use this P80 calculator for any material?

Yes, as long as you have sieve analysis data (% passing vs. size) for the particulate material, you can use this calculator to estimate P80.

What is F80?

F80 is similar to P80 but refers to the feed material – 80% of the feed particles are smaller than the F80 size.

How does P80 relate to the Bond Work Index?

The Bond Work Index (Wi) equation relates the energy required for grinding to the F80 (feed size) and P80 (product size). Knowing P80 and F80 allows you to calculate energy or vice-versa if Wi is known. See our Bond Work Index calculator.

What are typical P80 values in mining?

Typical P80 values for flotation feed range from 75 to 200 microns, depending on the ore and mineral liberation characteristics. Regrind circuits might target P80 values below 40 microns.

Related Tools and Internal Resources

• Bond Work Index Calculator: Calculate the Bond Work Index or energy required for grinding based on F80 and P80.
• Particle Size Distribution Calculator: Analyze more complex particle size data and fit distributions.
• Sieve Analysis Data Entry & Plotter: Input full sieve analysis data and visualize the distribution.
• Comminution Circuit Simulator: Model and simulate crushing and grinding circuits.
• Mineral Processing Formulas: A collection of useful formulas in mineral processing.
• Grinding Media Size Calculator: Estimate the optimal grinding media size.