Quick answer
SOH-CAH-TOA: sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse and tan θ = opposite ÷ adjacent. For a 30° angle and a hypotenuse of 10, the opposite side is 5 and the adjacent side 8.6603.
Enter an acute angle, a known side length and which side it is. The calculator returns the three sides. Use this sohcahtoa calculator to check your own figures.
Related tools: Trigonometry Calculator: All six trigonometric functions of an angle. Reference Angle Calculator: Acute angle between the terminal side and the x-axis. Inverse Sine Calculator: arcsin (inverse trigonometric function) with the result in degrees and radians.
How to use the SOHCAHTOA Calculator
- Enter acute angle (°) (between 0 and 89.999999).
- Enter known side length (above 0).
- Choose known side is the: Opposite side, Adjacent side and Hypotenuse.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Acute angle | A number, in ° | > 0, ≤ 89.999999 |
| Known side length | A number | > 0 |
| Known side is the | Choose one: Opposite side; Adjacent side; Hypotenuse | Starts at Hypotenuse |
Formula and method
Formula
sin θ = opp ÷ hyp; cos θ = adj ÷ hyp; tan θ = opp ÷ adj
IEEE-754 double precision; shown to at most 6 decimal places.
Solve the three ratios for the unknown sides.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Acute angle = 30; Known side length = 10; Known side is the = Hypotenuse.
| Result | Value |
|---|---|
| Opposite | 5 |
| Adjacent | 8.660254 |
| Hypotenuse | 10 |
Example 2
Inputs: Acute angle = 45; Known side length = 7; Known side is the = Adjacent side.
| Result | Value |
|---|---|
| Opposite | 7 |
| Adjacent | 7 |
| Hypotenuse | 9.899495 |
Example 3
Inputs: Acute angle = 60; Known side length = 6; Known side is the = Opposite side.
| Result | Value |
|---|---|
| Opposite | 6 |
| Adjacent | 3.464102 |
| Hypotenuse | 6.928203 |
The first line is the headline result (opposite). Below it the sOHCAHTOA Calculator lists adjacent and hypotenuse, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Worked example
opposite = 10 × sin 30° = 5; adjacent = 10 × cos 30° = 8.6603. Check: 5² + 8.6603² = 100 ✓.
Choosing the ratio
Use sine when the hypotenuse and opposite are involved, cosine for hypotenuse and adjacent, and tangent for the two legs. The angle must lie strictly between 0° and 90°.
How the result changes with acute angle
Holding every other input at the first worked example, this table changes only acute angle. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Acute angle | Opposite | Adjacent | Hypotenuse |
|---|---|---|---|
| 15 | 2.58819 | 9.659258 | 10 |
| 30 | 5 | 8.660254 | 10 |
| 60 | 8.660254 | 5 | 10 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Acute angle: entering "90" shows "Acute angle must be at most 89.999999." beside that field and no result.
Choosing between the SOHCAHTOA Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Trigonometry Calculator](/math/trigonometry-calculator/) | angle and unit | sin |
| [Reference Angle Calculator](/math/reference-angle/) | angle | Reference angle |
| [Inverse Sine Calculator](/math/inverse-sine/) | value | arcsin(0.5) |
| [Coterminal Angle Calculator](/math/coterminal-angle/) | angle | Smallest non-negative coterminal angle |
| [Cosine Calculator](/math/cosine-calculator/) | angle and unit | cos(60°) |
Background: trigonometry
In a right triangle, sin θ is the opposite side over the hypotenuse, cos θ the adjacent side over the hypotenuse and tan θ the opposite over the adjacent. Their reciprocals are cosecant, secant and cotangent. At 30° the values are sin = 0.5, cos = 0.866025 and tan = 0.577350.
Check the angle unit before you calculate: degrees convert to radians by multiplying by π/180, so 30° is about 0.5236 rad. Some values are undefined, for example tan 90°, because the cosine is zero there and the ratio would divide by zero.
Assumptions and limitations
- Angle strictly between 0° and 90°
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for acute angle to confirm this.
Frequently asked questions
How tall is a tree with a 30° angle at 20 m?
About 11.5 m, from 20 × tan 30°.
What does SOHCAHTOA mean?
A memory aid for the three ratios.
Does it work for non-right triangles?
No. SOHCAHTOA applies to right triangles; for other triangles use the sine rule or law of cosines.
What does the SOHCAHTOA Calculator calculate?
Find the other two sides of a right triangle from one side and an acute angle. It returns Opposite, Adjacent and Hypotenuse.
What formula does the SOHCAHTOA Calculator use?
sin θ = opp ÷ hyp; cos θ = adj ÷ hyp; tan θ = opp ÷ adj. Solve the three ratios for the unknown sides.
What do I need to enter in the sOHCAHTOA Calculator?
You enter Acute angle (°), Known side length and Known side is the.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Angle strictly between 0° and 90°.
What does the “Known side is the” option change?
It sets how the sOHCAHTOA is worked out. The choices are Opposite side, Adjacent side and Hypotenuse.
What is an example of a sOHCAHTOA result?
With acute angle 30, known side length 10 and known side is the Hypotenuse, the opposite is 5.
Related calculators
- Trigonometry Calculator — All six trigonometric functions of an angle.
- Reference Angle Calculator — Acute angle between the terminal side and the x-axis.
- Inverse Sine Calculator — arcsin (inverse trigonometric function) with the result in degrees and radians.
- Coterminal Angle Calculator — Angles sharing the same terminal side.
- Cosine Calculator — cos of an angle in degrees or radians.
- Angle of Elevation Calculator — Angle of elevation from a height difference and horizontal distance.
Sources
- Standard trigonometric definitions on the unit circle (NIST DLMF §4.14)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.