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Trigonometry

Cosine Calculator

cos(θ). Free online Cosine Calculator. Calculate cosine online — fast, accurate, mobile-friendly, no signup needed.

cos
0.5

Derivation

  1. ├── 01Givendeg = 60
  2. ├── 02Formulacos(t × π / 180)
  3. └── 03Compute cos0.5
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§01What is

Understanding the Cosine Calculator

The Cosine Calculator computes cos from 1 input: angle (°). cos(θ).

Trigonometry is how we turn angles into distances and distances into angles. It sits under every GPS fix, surveyor measurement, and game-engine render — and it still shows up in carpentry, roof pitches, and woodworking. The Cosine Calculator sits in that toolkit — it cos(θ). Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

cos(t × π / 180)

Where

deg
Angle (°)
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Angle (°) = 60.

  1. 01Start by noting the input — Angle (°): 60.
  2. 02Substitute these values into the formula: cos(t × π / 180)
  3. 03Compute cos: the calculator returns 0.5.
  4. 04Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Cosine Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Angle (°) halved

deg = 30 (from 60)

Keep every other input at its default and halve the angle (°). See how cos responds.

  1. 01New Angle (°): 30
  2. 02Baseline cos: 0.5
  3. 03New cos: 0.866025
  4. 04cos increases by 73.2% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Angle (°) doubled

deg = 120 (from 60)

Keep every other input at its default and double the angle (°). See how cos responds.

  1. 01New Angle (°): 120
  2. 02Baseline cos: 0.5
  3. 03New cos: -0.5
  4. 04cos decreases by 200% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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