Measure node imbalance, subtree heights, and structural stability. Get rotation hints and balanced tree checks. Export results fast with practical examples and helpful guidance.
Balance Factor: BF = Height of left subtree − Height of right subtree.
Absolute Imbalance: |BF| measures the size of height difference.
AVL Condition: A node is balanced when BF is -1, 0, or 1.
Rotation Logic: LL uses right rotation. RR uses left rotation. LR uses left-right rotation. RL uses right-left rotation.
Node Skew: This page also compares left and right subtree node counts for a broader structure check.
| Node | Left Height | Right Height | Left Child BF | Right Child BF | Left Nodes | Right Nodes | BF | Status | Rotation |
|---|---|---|---|---|---|---|---|---|---|
| A | 3 | 2 | 1 | 0 | 7 | 5 | 1 | Balanced for AVL | No rotation needed |
| B | 4 | 2 | 1 | 0 | 9 | 3 | 2 | Unbalanced for AVL | Right Rotation (LL case) |
| C | 2 | 4 | 0 | -1 | 4 | 8 | -2 | Unbalanced for AVL | Left Rotation (RR case) |
Tree balance factor is a core concept in binary tree analysis. It shows whether one subtree is taller than the other. A balanced node usually supports faster search, insert, and delete operations. This matters in AVL trees and other self-balancing structures. When the balance factor becomes too large, the tree shape drifts. That drift can reduce performance.
The usual formula subtracts right subtree height from left subtree height. A result of zero means equal heights. A positive result means the node is left heavy. A negative result means the node is right heavy. In AVL trees, acceptable values are -1, 0, and 1. Any larger gap suggests rebalancing.
An advanced tree balance factor calculator should do more than return one number. It should also inspect child balance factors. Those values help identify the likely rotation case. A left-heavy node with a left-heavy child usually points to an LL case. A left-heavy node with a right-heavy child usually points to an LR case. The same logic applies to RR and RL cases on the right side.
Subtree node counts add useful context. Two subtrees can have similar heights but very different node distributions. That can reveal uneven growth patterns. Comparing node share and skew gives a deeper structural view. This is helpful when studying binary search trees, AVL trees, and algorithm practice problems.
Use this calculator when reviewing manual tree exercises, debugging insertion logic, or learning balancing rules. It works well for classroom examples and coding tests. The result table is easy to export. The example table also helps you compare patterns quickly. If you track balance factor, subtree height, and rotation type together, tree analysis becomes much clearer and more reliable.
A tree balance factor is the difference between left subtree height and right subtree height at a node. It shows whether the node is left heavy, right heavy, or evenly balanced.
An AVL node is considered balanced when its balance factor is -1, 0, or 1. Values outside that range indicate the node needs rebalancing.
Child balance factors help identify the likely rotation type. They separate LL from LR cases and RR from RL cases during AVL rebalancing.
A positive value means the left subtree is taller than the right subtree. Larger positive values show stronger left-side imbalance.
A negative value means the right subtree is taller than the left subtree. Larger negative values show stronger right-side imbalance.
No. Node counts and heights measure different things. Heights decide the balance factor. Node counts only add supporting structure insight.
Most courses use left height minus right height. Some references reverse the sign. Always check your textbook or class convention before comparing answers.
Rotate when the node becomes unbalanced in an AVL tree. The required rotation depends on the node balance factor and the child balance direction.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.