Binary Tree Calculator

Calculator

Use one of the advanced modes below to calculate perfect tree metrics, full tree relations, general bounds, or traversals from an array view.

Calculation Mode

Levels

Levels count rows from the root.

Total Nodes

Use a full count such as 1, 3, 7, 15, or 31.

Leaf Nodes

Optional when internal nodes are provided.

Internal Nodes

Optional when leaf nodes are provided.

Actual Nodes

Optional. Adds fill ratio and fit checks.

Level-Order Array

Use commas between values. Write null for missing children.

Formula used

Perfect tree from levels:

Total Nodes = 2^L - 1, Leaf Nodes = 2^L-1, Internal Nodes = 2^L-1 - 1, Edges = Total Nodes - 1.

Perfect tree from nodes:

A perfect tree is exact only when Total Nodes + 1 is a power of 2. Then Levels = log₂(Nodes + 1).

Full tree relation:

For every full binary tree, Leaf Nodes = Internal Nodes + 1 and Total Nodes = 2 × Internal Nodes + 1.

General bounds:

For L levels, minimum nodes = L and maximum nodes = 2^L - 1. Maximum leaves at those levels = 2^L-1.

Array traversal mode:

The calculator treats the list as level order. For index i, left child = 2i + 1 and right child = 2i + 2.

How to use this calculator

1. Select the calculation mode that matches your problem.

2. Enter integers for structural modes, or provide a comma-separated array for traversal mode.

3. Click the calculate button. The result appears above the form, directly below the page header.

4. Review the metrics, inspect the Plotly chart, and export the output as CSV or PDF.

Example data table

Mode	Input	Selected Result	Output Example
Perfect Tree from Levels	Levels = 4	Total Nodes	15
Perfect Tree from Total Nodes	Total Nodes = 31	Levels	5
Full Tree Relation	Leaf Nodes = 9	Total Nodes	17
General Tree Bounds	Levels = 5, Actual Nodes = 19	Occupancy Ratio	61.29%
Traversal from Array	10, 7, 15, 5, 8, null, 20	Preorder	10, 7, 5, 8, 15, 20

FAQs

1) What does levels mean in this calculator?

Levels count horizontal rows from the root downward. A tree with only a root has one level and a height of zero edges.

2) What is the difference between a full tree and a perfect tree?

A full tree gives every internal node exactly two children. A perfect tree is full and also has every leaf at the same depth.

3) Why are some total node counts not valid for perfect trees?

Perfect trees must follow 2^L - 1. That creates counts like 1, 3, 7, 15, and 31. Other totals are not exact perfect sizes.

4) How does traversal mode interpret my list?

It reads the list as a level-order array. Missing children can be written as null, and child positions follow the index formulas shown above.

5) What makes a tree complete?

A complete tree fills every level from left to right, except possibly the last. There cannot be a gap before a later node appears.

6) Can I use text labels instead of numbers in traversal mode?

Yes. You may enter symbols, names, or numbers. Traversal mode treats each non-null entry as a node label.

7) What does occupancy ratio mean?

Occupancy ratio compares actual nodes with the maximum nodes possible for the selected levels. It shows how full the structure is as a percentage.

8) Why are CSV and PDF exports useful here?

They let you keep a copy of calculated metrics for homework, planning, reviews, or quick sharing without retyping the results.