Angle Dilation Calculator

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Need a quick way to calculate a dilated angle? This Angle Dilation Calculator finds the new angle when scaling an original angle by a specific factor. Dilation refers to proportionally increasing or decreasing an angle while keeping its origin intact.

Whether working in degrees or radians, this tool provides clear and accurate results to simplify your calculations. Perfect for students, professionals, or anyone exploring angle transformations!

What Is Angle Dilation?

A dilation angle refers to the result of scaling an original angle by a specific factor, known as the dilation factor or scale factor. This process involves proportionally increasing or decreasing the original angle while maintaining its geometric relationships or orientation.

How to Calculate a Dilated Angle?

To find a dilated angle, multiply the original angle by a specific factor. You can show this mathematically with the following formula:

Ad = Ao × Df

Where:

• Ad: Dilated angle (the result)
• Ao: Original angle
• Df: Dilation factor (scale factor)

The dilation factor determines how much the original angle is scaled. A Df>1 increases the angle, while Df<1 reduces it.

Example 1: Dilating an Angle in Degrees

Given:

• Original angle (Ao) = 45°
• Dilation factor (Df) = 2

Calculation:

Ad = 45° × 2 = 90°

Result: The dilated angle is 90°.

Example 2: Dilating an Angle in Radians

Given:

• Original angle (Ao) = π/4 radians
• Dilation factor (Df) = 3

Calculation:

A(d) = π/4 × 3 = 3π/4 radians

Result: The dilated angle is 3π/4 radians or approximately 2.36 radians.

Dilated Angle Table

This table shows the calculated dilated angle for given original angles and dilation factors.

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Double angle calculator

Coterminal angle calculator

Reference angle calculator

FAQs:

Can dilation be applied to angles in radians?

Yes, dilation works for angles in both degrees and radians. Simply use the same formula. For example, if the original angle is π/4 radians and the dilation factor is 2, the dilated angle is (π/4) × 2 = π/2 radians.

What happens if the dilation factor is less than 1?

When the dilation factor is less than 1, the original angle is reduced in size. For example, if the original angle is 120° and the dilation factor is 0.5, the resulting dilated angle is 120 × 0.5 = 60°

Can a dilated angle exceed 360°?

Yes, if the dilation factor is large. The resulting angle can be more than 360°. In these cases, the angle can be adjusted to fit within the range of 0° to 360°.