What is B-tree order (minimum degree)?

The minimum degree t determines node capacity. Every non-root node holds between t-1 and 2t-1 keys, and has between t and 2t children. A higher t means each node stores more keys, reducing tree height but increasing node scan cost.

What is the difference between minimum and maximum depth?

Minimum depth occurs when every node is completely full (2t-1 keys). Maximum depth occurs when every node is at minimum capacity (t-1 keys, except the root which can hold just 1). Real trees fall somewhere between these bounds.

Why does depth matter for database performance?

Each level of a B-tree typically requires one disk or buffer-pool read. A tree of depth 3 needs at most 3 I/O operations to find any key. Keeping depth low is why databases use large page sizes — more keys per page means higher order and shallower trees.

What order does PostgreSQL or MySQL use?

PostgreSQL uses 8 KB pages by default; an index on a 4-byte integer fits roughly 400 keys per leaf page, giving an effective order of ~200. MySQL InnoDB's 16 KB pages fit even more. These high orders keep real-world B-tree depths at 3–4 levels for millions of rows.

Is this tool for B-trees or B+ trees?

The depth formula applies to both. B+ trees store all data in leaf nodes, but the internal node structure follows the same height bounds. Real database indexes are almost always B+ trees, but the depth calculator is valid for either variant.

What does "number of keys" mean?

It is the total count of unique key entries in the index — roughly equal to the number of indexed rows. For a primary key index on a table with 1 million rows, enter 1,000,000.

B-Tree Depth Calculator

Name: B-Tree Depth Calculator
Availability: InStock
Author: Nham Vu

Enter your B-tree order and key count to instantly see minimum and maximum tree depth, node counts, and read I/O estimates.

B-Tree Parameters

Minimum Degree (t)

Each non-root node holds t−1 to 2t−1 keys. Common DB values: 50–500.

Number of Keys (n)

Total indexed rows or key entries in the tree.

Enter B-tree parameters and press Calculate

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Summary

Enter your B-tree order and key count to instantly see minimum and maximum tree depth, node counts, and read I/O estimates.

How it works

Enter the B-tree order (minimum degree t), which defines the minimum and maximum children per internal node.
Enter the total number of keys stored in the tree.
The tool computes the minimum depth: floor(log base 2t of ((n+1)/2)).
It also computes the maximum depth: floor(log base t of ((n+1)/2)).
Node and I/O estimates are derived from the depth bounds.
Use the results to compare index configurations or predict lookup cost at scale.

Use cases

Estimate worst-case disk reads for a B-tree index lookup in PostgreSQL or MySQL.
Compare branching factors when choosing between page sizes for an InnoDB table.
Teach the relationship between B-tree order, key count, and tree height.
Predict how many levels a B+ tree index will need after ingesting millions of rows.
Validate assumptions about index depth when profiling slow queries.
Understand why doubling the page size (higher order) reduces tree depth.
Calculate the theoretical node count range for capacity planning.
Explain B-tree height guarantees (O(log n)) in system design interviews.

Frequently Asked Questions

Last updated: 2026-07-22 · Reviewed by Nham Vu