🏛️ Arch Calculator
Calculate arch dimensions for construction projects
Width of arch opening at base
Height from base to arch center
How to Use This Calculator
Enter Span
Input the span (width) of the arch opening in feet. This is the horizontal distance across the arch at its base.
Enter Rise
Input the rise (height) of the arch in feet. This is the vertical distance from the arch base to the highest point (center). Rise must be less than half the span.
Calculate and Review
Click "Calculate Arch Dimensions" to see the arch radius, length, central angle, and area. Use these values for construction planning and material estimation.
Formula
Radius = (Span² + 4 × Rise²) / (8 × Rise)
Central Angle = 2 × arcsin(Span / (2 × Radius))
Arch Length = Radius × Central Angle
Example: 10 ft span with 2 ft rise
Step 1: Radius = (10² + 4 × 2²) / (8 × 2) = (100 + 16) / 16 = 7.25 feet
Step 2: Central Angle = 2 × arcsin(10 / (2 × 7.25)) = 89.0°
Step 3: Arch Length = 7.25 × (89.0° × π/180) = 11.27 feet
About Arch Calculator
The Arch Calculator is an essential tool for masons, architects, contractors, and builders who need to calculate arch dimensions for construction projects. This calculator eliminates guesswork by providing precise arch calculations based on span and rise, helping you plan arches for doorways, windows, bridges, and decorative elements.
When to Use This Calculator
- Arch Construction: Calculate arch dimensions for brick, stone, or concrete arches
- Doorway Design: Plan arched doorways and openings
- Window Planning: Design arched windows and openings
- Material Estimation: Calculate materials needed for arch construction
- Decorative Elements: Plan decorative arches and architectural features
Why Use Our Calculator?
- ✅ Accurate Calculations: Precise arch calculations using standard geometric formulas
- ✅ Multiple Dimensions: Calculates radius, length, angle, and area
- ✅ Multiple Units: Shows results in feet and inches
- ✅ Time Savings: Instant calculations eliminate manual math
- ✅ Easy to Use: Simple input fields for span and rise
Understanding Arch Dimensions
Span: The horizontal width of the arch opening at its base. This is the distance between the two support points where the arch rests.
Rise: The vertical height from the arch base to the highest point (center). Rise must be less than half the span for a valid arch. Higher rise creates a more pronounced arch shape.
Radius: The radius of the circular arc that forms the arch. This is calculated based on span and rise using geometric formulas. The radius determines the curvature of the arch.
Tips for Best Results
- Measure Accurately: Use accurate span and rise measurements for precise calculations
- Check Rise Limit: Rise must be less than half the span for a valid arch
- Consider Material: Different materials may require different arch designs
- Account for Support: Ensure adequate support for arch loads
- Consult Engineers: For structural arches, consult a structural engineer
Frequently Asked Questions
What is arch span and rise?
Span is the horizontal width of the arch opening at its base. Rise is the vertical height from the arch base to the highest point (center). These two measurements define the arch shape.
How do I calculate arch radius?
Arch radius = (Span² + 4 × Rise²) / (8 × Rise). The calculator performs this calculation automatically based on your span and rise values.
What is the maximum rise for an arch?
Rise must be less than half the span for a valid arch. For example, a 10-foot span can have a maximum rise of less than 5 feet. Higher rises create more pronounced arches.
How do I calculate arch length?
Arch length = Radius × Central Angle (in radians). The calculator automatically calculates arch length based on span and rise, showing the length along the curved arch surface.
Can I use this for different arch types?
This calculator uses circular arch formulas, which are most common. For elliptical or other arch types, consult specialized formulas or architectural software.