Updated · Methodology: named formula library
Law of Cosines Calculator
Solve a triangle given SAS or SSS.
Value A to Value B = 4:1 (4 as decimal).
Why This Calculation Matters
The Law of Cosines Calculator gives you a fast, accurate answer for law of cosines, useful for homework, coursework, or inside a larger problem. The formula is shown below so you can see exactly what the tool is doing and verify it against a textbook or other reference.
How to Use This Calculator
- Enter your values in the input fields, each one has a label and help text explaining what to type.
- Results appear instantly as you type; there's no "calculate" button to press.
- Change any input to compare scenarios side by side.
All math happens in your browser. Nothing you type is sent to a server, saved, or shared.
How to Use
Enter values in the fields on the left. Results update as you type, no submit button needed.
Understanding Results
Each output shows the calculated figure plus a breakdown of contributing inputs. Compare scenarios by editing any value.
Accuracy Notes
Every Law of Cosines Calculator on CalcIntel uses a documented formula. Results are estimates, real outcomes depend on assumptions and market conditions not captured in a simplified calculation.
Formula
c² = a² + b². Given any two sides of a right triangle, the third is solvable: c = √(a² + b²), or a = √(c² − b²).
Worked Example
100 Value A to 25 Value B
- a
- 100
- b
- 25
- Result
- 4:1 (4.00)
100 / 25 = 4.00. Simplified: 4:1.
When to Use This Calculator
- Check homework, textbook problems, or coursework answers.
- Explore how the result changes as you vary inputs, great for intuition building.
- Verify a calculation inside a larger engineering, research, or data workflow.
Limitations & Common Mistakes
- Results are only as accurate as the inputs, double-check rounding and units.
- Numeric precision is limited by JavaScript floating-point arithmetic.
Frequently Asked Questions
How is the Law of Cosines Calculator computed?
Value A divided by Value B, plus a simplified ratio (e.g., 4:3) using greatest common divisor. Both decimal and ratio forms are useful in different contexts: decimal for math, ratio form for comparisons or recipe scaling.
What does Value A:Value B mean?
It's a comparison: for every Value B unit, you have a corresponding amount of Value A. Useful when the absolute numbers matter less than the proportion (e.g., reading 8:1 LTV/CAC immediately tells you the unit economics are healthy without needing the dollar amounts).
Why simplify the ratio?
4:3 is more readable than 200:150. The simplified form (using greatest common divisor) preserves the proportion while making it easier to interpret. Common simplified ratios: 16:9 (widescreen), 4:3 (legacy displays), 3:1 (LTV:CAC for SaaS).
When is a ratio more useful than the absolute values?
Comparison across scales. A $1B company and a $1M company can both have a 3:1 LTV:CAC; the ratio reveals comparable unit economics regardless of scale. Use ratios for benchmarking; use absolute numbers for budgeting.
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