Secant Calculator
Calculate the secant of any angle. Secant is the reciprocal of cosine: sec(θ) = 1/cos(θ).
This free online secant calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.
Results
sec(θ)
1.154701
Angle (radians)
0.523599 rad
How to Use This Calculator
Enter your input values
Fill in all required input fields for the Secant Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.
Review your inputs
Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.
Read the results
The Secant Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.
Explore parameter sensitivity
Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.
Formula Reference
Secant Calculator Formula
See calculator inputs for the governing equation
Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.
When to Use This Calculator
- •Use the Secant Calculator when you need a quick mathematical result without writing out all the steps manually, saving time on repetitive calculations.
- •Use it to verify hand calculations on tests or assignments and catch arithmetic mistakes.
- •Use it when teaching or explaining mathematical concepts to others, demonstrating how changing inputs affects the result.
- •Use it to explore the behavior of mathematical functions across a range of inputs.
About This Calculator
The Secant Calculator is a free mathematical calculation tool for students, educators, and professionals who need quick, reliable results. Calculate the secant of any angle. Secant is the reciprocal of cosine: sec(θ) = 1/cos(θ). The underlying algorithms implement well-established mathematical formulas and numerical methods. Results are computed instantly in the browser. This tool is useful for learning, verification of hand calculations, and rapid exploration of mathematical relationships. All computation happens locally — no data is sent to a server.
About Secant Calculator
The secant function is the reciprocal of the cosine function: sec(θ) = 1/cos(θ). In a right triangle, it equals the ratio of the hypotenuse to the adjacent side. Secant is undefined at 90° and 270° (where cosine equals zero) and has a minimum absolute value of 1. The secant function has a period of 360° (2π radians) and is an even function: sec(−θ) = sec(θ). While secant is less commonly used in everyday calculations than sine, cosine, or tangent, it plays an important role in calculus, particularly in integration and trigonometric substitution. The integral of secant, ∫ sec(x) dx = ln|sec(x) + tan(x)| + C, is historically significant and was one of the key results needed for the Mercator map projection. This calculator computes the secant for any angle.
The Math Behind It
Formula Reference
Secant Function
sec(θ) = 1 / cos(θ) = hypotenuse / adjacent
Variables: θ = angle
Worked Examples
Example 1: Secant at standard angles
Compute sec(60°).
sec(60°) = 2
Common Mistakes & Tips
- !Trying to compute sec(90°) — it is undefined since cos(90°) = 0.
- !Confusing secant with cosecant — sec = 1/cos, csc = 1/sin.
- !Expecting sec(θ) to be between −1 and 1 — secant values are always |sec(θ)| ≥ 1 or undefined.
Related Concepts
Used in These Calculators
Calculators that build on or apply the concepts from this page:
Frequently Asked Questions
What is the range of the secant function?
sec(θ) can take any value in (−∞, −1] ∪ [1, ∞). It is never between −1 and 1.
Why is secant important in calculus?
The identity 1 + tan²(θ) = sec²(θ) appears in many integrals, and trigonometric substitution x = a sec(θ) handles integrals involving √(x² − a²).