Advanced Peak and Trough Calculator

Calculator Inputs

Example Data Table

Formula Used

Peak rule: A point is a peak when xᵢ > xᵢ₋₁ and xᵢ > xᵢ₊₁ in strict mode.

Trough rule: A point is a trough when xᵢ < xᵢ₋₁ and xᵢ < xᵢ₊₁ in strict mode.

Smoothing: MAᵢ = sum(values inside selected window) / number of values inside selected window.

Prominence: min(|MAᵢ - MAᵢ₋₁|, |MAᵢ - MAᵢ₊₁|). Points below the threshold are ignored.

Amplitude: |peak value - trough value|. Average amplitude uses alternating detected turning points.

Trend slope: A simple linear regression slope estimates the overall direction across all ordered values.

How to Use This Calculator

1. Paste values in time order. You may enter labels with values.
2. Enter a unit label, such as sales, visits, volts, or points.
3. Use smoothing window 1 for raw data. Increase it for noisy data.
4. Set minimum prominence to remove small, weak movements.
5. Set minimum distance to prevent crowded turning points.
6. Submit the form and review the result section above the form.
7. Download the table as CSV or PDF for later reporting.

Understanding Peaks And Troughs

A peak is a high turning point in a series. A trough is a low turning point. These points help explain movement. They show where growth slowed, reversed, or gained strength. The calculator studies numeric values and marks local highs and lows. It can work with sales, traffic, prices, temperatures, scores, workloads, or any ordered data.

Why Turning Points Matter

Raw numbers can feel noisy. A clear peak or trough gives a useful reference. A peak can show strong demand, high stress, or a possible limit. A trough can show weak demand, low activity, or a recovery base. When you compare both points, you can measure the size of each swing. You can also study how often cycles repeat.

Using Smoothing And Prominence

Real data often contains random jumps. Smoothing reduces small bumps by averaging nearby values. This makes the main pattern easier to see. Prominence adds another filter. It tells the calculator to ignore tiny changes that do not matter. A higher prominence value finds fewer, stronger turning points. A lower value finds more sensitive signals.

Reading The Results

The result table lists each detected point. It shows the position, label, type, original value, smoothed value, and nearby change. Peaks and troughs are also summarized with averages and extremes. The amplitude result shows the average distance between alternating turning points. The trend estimate gives a quick direction check across the whole series.

Best Practices

Use values in the correct order. Choose a smoothing window of one for clean data. Increase it when the series is noisy. Set a small prominence first. Raise it until minor bumps disappear. Keep the minimum distance low for short cycles. Increase it when points appear too close together. Review the chart or table after calculation. Export the results for reports, dashboards, or further analysis.

Common Uses

This method is useful beyond finance. Website owners can inspect traffic seasons. Teachers can review test score waves. Project managers can locate workload spikes. Store owners can compare busy and quiet periods. Fitness users can review performance cycles. The same idea works whenever values rise, fall, and rise again over time in clear order.

FAQs