Angle Cuts — Miter, Bevel & Compound for Carpentry
Compute miter and bevel angles for crown molding, rafters, picture frames, and trim. Supports compound miters with spring angle, simple miters, bird's mouth cuts, and rafter geometry. Provides saw gauge and blade tilt settings.
Why This Construction Metric Matters
Why: Correct miter and bevel angles ensure tight joints in crown molding, rafters, and trim. Wrong angles cause gaps and misalignment. Compound cuts require both miter gauge and blade tilt; this calculator provides both.
How: Simple miter: 90° − (corner/2). Crown: miter = arctan(cos(spring)×tan(corner/2)), bevel = arcsin(sin(spring)×sin(corner/2)). Rafter: uses roof pitch and hip angle. Bird's mouth: seat and plumb from pitch.
- ●38° spring angle is most common for US crown molding.
- ●Test cuts on scrap before cutting finished material.
- ●Compound saw: set miter first, then bevel.
- ●Bird's mouth depth typically 1/3 of rafter depth.
Compact Examples
Cut Type
Compound Miter
Combined miter and bevel cut for crown molding and complex angles
Selected: 38° (Standard) (38°) - Most common crown molding
Standard: 90° for square corners
For reference only
Results
Miter Angle
38.24°
Bevel Angle
25.81°
Compound Angle
46.13°
Blade Angle
25.81°
Effective Angle
46.13°
Back Cut Angle
64.19°
🔧 Saw Settings
Miter Gauge
38.24°
Set miter saw to this angle
Blade Tilt
25.81°
Tilt blade to this angle
Fence Angle
38.00°
For crown molding setup
📐 Visual Angle Diagram
Miter: 38.24°
Bevel: 25.81°
Charts
📊 Angle Comparison
🏠 Roof Pitch
📐 Angle Distribution
📈 Pitch Progression
Step-by-Step Calculation
=== Angle Cut Calculation === Cut Type: Compound Miter Corner Type: Inside Corner Corner Angle: 90° === Compound Miter Calculation === Spring Angle: 38° Corner Half-Angle: 45° Miter Formula: arctan(cos(38°) × tan(45°)) Miter Angle = 38.24° Bevel Formula: arcsin(sin(38°) × sin(45°)) Bevel Angle = 25.81° === Final Results === Miter Angle: 38.24° Bevel Angle: 25.81° Compound Angle: 46.13° Blade Angle: 25.81° Effective Angle: 46.13° Back Cut Angle: 64.19° === Saw Settings === Miter Gauge Setting: 38.24° Blade Tilt Setting: 25.81° Fence Angle: 38.00°
Planning estimates only. Verify with a licensed engineer or contractor before construction.
📐 Construction Industry Facts
90° corner → 45° miter (simple)
— Geometry
Crown: spring angle affects both miter and bevel
— Carpentry
Rafter cuts use roof pitch and hip angle
— IRC
Bird's mouth: seat cut + plumb cut
— Framing
📋 Key Takeaways
- • Simple miter: 90° − (corner/2) | 90° corner → 45° miter
- • Crown: Miter = arctan(cos(spring)×tan(corner/2)), Bevel = arcsin(sin(spring)×sin(corner/2))
- • Spring angles: 38° (common), 45°, 52° (European)
- • Bird's mouth: Seat = arctan(1/tan(pitch)), Plumb = roof pitch angle
Did You Know?
Miter = horizontal angle; bevel = blade tilt. Compound = both.
Source: Carpentry
38° spring angle is most common for US crown molding.
Source: Trim
6/12 pitch = 26.57°. 12/12 = 45°. Ratio = rise/run.
Source: Roof framing
Bird's mouth: seat cut on wall plate, plumb cut at ridge.
Source: Rafters
Inside 90° corner: each piece cut at 45° miter.
Source: Frames
Bevel-only: single blade tilt, no miter rotation.
Source: Chamfers
How Angle Cuts Are Calculated
Simple miter: half the corner. Crown: trig with spring angle. Rafter: trig with pitch and hip angle.
Simple Miter
Miter = 90° − (corner / 2)
Crown Molding
Miter = arctan(cos(spring)×tan(corner/2))
Expert Tips
Test Cuts
Cut scrap first to verify angles.
Crown Setup
Set fence to spring angle.
Mark Orientation
Top/bottom, inside/outside.
Safety
Clamp work, use guards.
Spring Angle Comparison
| Spring Angle | Degrees | Use |
|---|---|---|
| 30° (Low Profile) | 30° | Low profile crown |
| 35° (Custom) | 35° | Custom applications |
| 38° (Standard) | 38° | Most common crown molding |
| 45° (Common) | 45° | Standard crown molding |
| 52° (European) | 52° | European-style crown |
Frequently Asked Questions
What is spring angle for crown molding?
Spring angle is the angle the crown sits against the wall and ceiling. 38° and 45° are most common in the US.
What miter angle for a 90° corner?
For simple miter: 45° each side. Formula: Miter = 90° − (corner angle / 2).
Inside vs outside corner—same formula?
Yes, same formula. Inside is concave; outside is convex. Orientation differs but angles are calculated the same.
How do I calculate bird's mouth seat cut?
Seat = arctan(1/tan(pitch)). Plumb cut equals the roof pitch angle.
What is hip rafter miter formula?
Miter = arctan(tan(pitch)/sin(hip)). Bevel = arctan(sin(pitch)×tan(hip)).
Compound miter vs simple miter?
Compound: miter + bevel (crown molding). Simple: miter only (picture frames, baseboards).
Key Numbers
📚 Sources
⚠️ Disclaimer: Angles are calculated values. Verify with test cuts. Saw calibration and material variations affect results.
Related Calculators
Miter Angle Calculator
Calculate precise miter angles for frames, trim, and polygon projects. Supports custom angles, polygon calculations, kerf compensation, and multiple joint...
ConstructionAngle of Depression Calculator
Calculate angle of depression from heights and distances. Supports multiple calculation modes including from heights, from angle, and from slope percentage....
ConstructionBirdsmouth Cut Calculator - Rafter Seat Cut Dimensions
Calculate birdsmouth cut dimensions for rafters including seat depth, heel height, and plumb cut angle. Essential for proper rafter-to-plate connections in...
ConstructionRafter Length Calculator - Roof Framing Dimensions
Calculate rafter length, run, rise, and overhang dimensions for roof framing. Supports common, hip, valley, and jack rafters with birdsmouth cut calculations.
ConstructionAir Changes Per Hour Calculator - Ventilation & HVAC Design
Calculate air changes per hour for proper ventilation and HVAC design. Determine if your room meets recommended ACH standards for different room types...
ConstructionAir Conditioner BTU Calculator - AC Sizing & Capacity
Calculate the required BTU capacity for air conditioning based on room size, sun exposure, insulation quality, climate zone, occupants, and appliances. Get...
Construction