Solve X Calculator

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Fact Checked and Reviewed by David Chen, CFA

Use this Solve X Calculator to find the missing variable in your break-even equation. Whether you need to determine the required price, quantity, or cost structure, this tool provides instant and accurate results for business planning.

Solve X Calculator

Leave one field empty to solve for it. At least 3 values are required.

Result
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solve x calculator Formula:

P × Q = F + (V × Q)

Source: Investopedia – Break-Even Analysis | Harvard Business Review

Variables:

  • Quantity (Q): The total number of units produced or sold.
  • Price per Unit (P): The selling price for each individual unit.
  • Variable Cost (V): Costs that change in proportion to production volume (e.g., raw materials).
  • Fixed Costs (F): Business expenses that remain constant regardless of production (e.g., rent, salaries).

What is solve x calculator?

The Solve X Calculator is an algebraic utility designed to find the break-even point or any missing variable in a linear business equation. In economics, the break-even point is the moment where total revenue equals total costs, resulting in zero profit or loss.

By isolating variables like Quantity or Fixed Costs, business owners can perform “What-If” scenarios to determine the feasibility of new products or price adjustments. This calculator handles the complex shifting of terms across the equals sign automatically.

How to Calculate solve x calculator (Example):

  1. Identify the known values: e.g., Fixed Cost = $10,000, Price = $100, Variable Cost = $60.
  2. Leave the unknown (X) empty: in this case, Quantity (Q).
  3. Apply the rearranged formula: $Q = F / (P – V)$.
  4. Substitute values: $10,000 / ($100 – $60) = 10,000 / 40$.
  5. Result: $250$ units.

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Frequently Asked Questions (FAQ):

What if the variable cost is higher than the price?

If $V > P$, the business will lose money on every unit sold. The calculator will show an error or a negative value, indicating the model is unsustainable.

Why is fixed cost important in this formula?

Fixed costs represent the hurdle that must be overcome by the “contribution margin” ($P – V$) to reach profitability.

Can I use this for service businesses?

Yes, simply treat “units” as hours or projects, and variable costs as direct labor or material costs per project.

Is the break-even point the same as profit?

No, the break-even point is where profit is exactly zero. Any unit sold beyond this point contributes to net profit.