---
title: "Alligation — Method, Calculator, and Practice Problems"
description: "Alligation explained with the tic-tac-toe grid, a pharmacy-native calculator, and unlimited practice problems with worked solutions. Includes its 2026 PTCE status."
updated: 2026-08-03
canonical: https://ptcbready.com/pharmacy-tech-math/alligation
source-hash: 5ee2ee4f9d0222a4
sources:
  - "PTCB — PTCE content outline (2026 update removing alligation)": https://www.ptcb.org/credentials/certified-pharmacy-technician
---

# Alligation — Method, Calculator, and Practice Problems

> Alligation explained with the tic-tac-toe grid, a pharmacy-native calculator, and unlimited practice problems with worked solutions. Includes its 2026 PTCE status.

## 2026 PTCE status

Alligation was REMOVED from the PTCE content outline effective January 6, 2026. It remains on this site because employers, compounding work, and older study materials still use it — but it is no longer tested.

## The grid method

Set up the tic-tac-toe grid: higher strength top-left, lower strength bottom-left, desired strength in the center. Subtract diagonally (ignore signs) to get PARTS of each component, then scale parts to the batch volume.

**parts (high) = desired − low · parts (low) = high − desired**

## Worked example (computed)

**Problem.** You need 100 mL of a 50% solution, prepared by mixing 70% and 20% stock solutions. How many mL of the 20% solution are needed?

1. parts of 70% = 50 − 20 = 30 — Alligation grid: the higher strength's parts = desired minus lower (read diagonally).
2. parts of 20% = 70 − 50 = 20 — The lower strength's parts = higher minus desired.
3. total parts = 30 + 20 = 50 — Add the parts to get the total.
4. 100 mL × 20/50 = 40 mL of 20% — Multiply the batch volume by the 20% share of total parts.

**Answer: 40 mL.**

## Common traps

- Reading the diagonal backwards (reporting the other component's volume).
- Stopping at parts without scaling to the batch volume.

The interactive calculator draws the grid for any inputs: https://ptcbready.com/pharmacy-tech-math/alligation

---
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Cite as: PTCB Ready, updated 2026-08-03. Interactive version: https://ptcbready.com/pharmacy-tech-math/alligation