Calculadora de Arcos
Calcule al instante radio, cuerda de giro, ángulo central, dovelas y tablas de coordenadas de replanteo en obra.
Tabla de Coordenadas de Replanteo y Trazador
For large arches where the swing radius exceeds your compass or room length. Simply draw your baseline, measure out horizontal intervals from center (X), and mark vertical height (Y) to plot perfect curves directly on wood or wall.
| Pt # | Dist from Center (X) | Height (Y) | Fracción | Drop |
|---|
Simulador de Trazo en Contrachapado
🔨 Carpentry Technique: Tap finish brads at coordinate marks. Bend a flexible batten against the pins to scribe a smooth curve.
¿Qué es una Calculadora de Arcos?
An Arch Calculator is a specialized construction geometry tool designed to solve the physical dimensions required to draw, frame, template, or build curved architectural structures from span and rise.
In construction trades, manual calculations often introduce compounding errors. A difference of just 1/4" in sagitta can cause flexible moulding to buckle or masonry voussoirs to misalign.
Simulador Interactivo de Teorema de Cuerdas
💡 Nota de Obra: El centro de curvatura desciende por debajo de la línea de arranque a medida que la flecha disminuye en arcos rebajados.
Cómo Usar la Calculadora de Arcos
From taking rough opening measurements on the jobsite to stepping out coordinate curves onto 3/4" plywood templates in 4 straightforward steps.
Profile & Trade Configuration
Haga clic en los diferentes perfiles geométricos para ver cómo se adapta nuestro motor de cálculo a arcos de medio punto, rebajados, elípticos u ojivales.
Cómo Funciona — Fórmulas y Ecuaciones
Clean geometric equations with real-time interactive vector annotations. Click or hover any formula variable to highlight its physical dimension.
Euclidean Chord Theorem Geometry
The radius of the circular arc. Because the center of curvature lies below the springline baseline, the swing arm extends distance R from pivot (C) to apex (A).
Radius from Span & Rise
Derived from Euclid's intersecting chords theorem:
Y(X) = √(R² - X²) - (R - H)
Hover over variables above to highlight corresponding geometry.
Arc Length & Central Angle
Calculate the perimeter curve distance along the soffit and total angular sweep:
θ (deg) = θ (rad) × (180 / π)
L (Arc) = R × θ (rad)
Essential for ordering flexible trim, drywall bead, or bending formwork ribs.
Elliptical Axes & Focal Points
Semi-major axis a, semi-minor axis b, and pin focus distance c:
c (Focus) = √(a² - b²)
P ≈ π × [3(a+b) - √((3a+b)(a+3b))]
String length for layout equals full span (W).
Dynamic Worked Example: Test Your Custom Values
Apply chord theorem:
R = 45.00 inches
Half-chord arcsine:
θ = 106.26° (1.855 rad)
Radius × Radians:
L ≈ 83 7/16" (83.48")
Cut dimensions:
Radius Center: -27.0" drop
7 Tipos Esenciales de Arcos y Simulador de Empuje
Compare mathematical formulas, structural thrust characteristics, and live compressive load vectors across the 7 fundamental arch profiles.
Segmental Arch Profile
Shallow circular chord arches create intense horizontal outward forces (thrust) at the springline, requiring substantial wall backing or reinforced abutments.
Segmental Arch
Shallow circular arc less than 180°
Semicircular (Roman) Arch
Full 180° half-circle where Rise = Half Span
Elliptical Arch
True semi-ellipse or 3/5-centered compound curve
Gothic (Pointed / Equilateral)
Two intersecting circular arcs meeting at an apex point
Tudor (Four-Centered) Arch
Compound 4-radius curve with pointed apex and low rise
Horseshoe (Moorish / Keyhole)
Circular arc exceeding 180° with inwards-curving imposts
Jack / Flat Lintel Arch
Horizontal soffit supported by angled skewback voussoirs
Matriz Comparativa de Tipos de Arcos
Compare geometric construction, structural load characteristics, and framing difficulty across all architectural arch shapes.
| Arch Style | Geometry Base | Rise-to-Span | Structural Thrust | Difficulty | Typical Application |
|---|---|---|---|---|---|
| ◒ Segmental | Single shallow circular arc (center below springline) | 1:3 to 1:6 | High lateral kick (requires abutments) | Easy | Interior room dividers, brick window heads |
| ◐ Semicircular (Roman) | Full 180° semicircle (Radius = Span/2) | Exact 1:2 | Balanced vertical load (zero kick) | Easy | Classical architecture, Roman aqueducts, arches |
| ⬭ Elliptical | True mathematical ellipse (major & minor axes) | Flexible | Smooth compression distribution | Moderate | Cased openings, luxury custom trim, carriage doors |
| ⋀ Gothic / Pointed | Dual intersecting circular arcs meeting at crown | 1:1 to 2:1 | Directs thrust sharply downward | Moderate | Cathedrals, ecclesiastical windows, tall gates |
| ⌒ Tudor (4-Centered) | Four distinct radius centers (2 tight, 2 flat) | 1:3 | Moderate lateral thrust | Advanced | English Tudor fireplaces, estate entry gates |
| ☉ Horseshoe (Moorish) | Circular arc extending beyond 180° | > 1:2 | Inward pinching at neck springline | Advanced | Islamic, Moorish, and Spanish revival architecture |
| ▭ Jack / Flat Arch | Flat horizontal soffit with angled skewback bricks | 0 (Flat) | Extremely high lateral kick (Requires Buttress) | Advanced | Georgian brick window lintels, fireplace surrounds |
Best for: Interior room dividers, brick window heads, shallow porch headers.
Anatomía de un Arco — Terminología y Geometría
Click or hover over any term or interact with diagram hotspots to inspect key architectural components.
The central wedge-shaped stone or framing gusset at the crown locking the arch into compression.
The central wedge-shaped stone or framing gusset at the crown locking the arch into compression.
The inner, bottom concave surface of the arch opening determining clear walk-through height.
The upper, exterior convex curved boundary of the arch ring or framing plate.
The wedge-shaped masonry units or segmented framing blocks forming the curved arch ring.
The imaginary horizontal baseline from which the curve begins springing away from vertical jambs.
The inclined or horizontal seating surface on piers bearing outward diagonal arch thrust.
Límites de Materiales y Construcción en Obra
Designing an arch is only half the battle. Building it requires accounting for physical material bend limits, formwork deflection, and masonry thrust lines.
Drywall & Trim Bending Stress Simulator
1/4" High-Flex Drywall can bend completely dry to a 30" radius without wetting or steaming.
Minimum Bending Radii for Soffit Linings
Gypsum Assoc. GA-216Never attempt to bend sheet materials beyond manufacturer elastic limits. If your calculated arch radius is tighter than the minimums below, kerf the substrate or use multi-layered flexible gypsum:
| Material Type | Min Radius | Jobsite Recommendation |
|---|---|---|
| 1/4" Flexible Drywall (Dry) | 24 inches (610 mm) | Double-layer required for fire and structural rigidity. |
| 1/4" Flexible Drywall (Wet/Steamed) | 12 inches (305 mm) | Moistened on back paper; fastened with fine drywall screws. |
| 3/8" Standard Drywall (Dry) | 72 inches (1828 mm) | Requires gradual bend along lengthwise grain. |
| 1/2" Standard Drywall (Dry) | 120 inches (3048 mm) | Only suitable for broad segmental room transitions. |
| 1/4" Kerfed MDF / Bendable Plywood | 8 inches (203 mm) | Ideal for tight radius soffits and arch window jamb returns. |
Use 3/4" CDX or birch plywood for arch ribs spaced max 16" on center. Skin the soffit with two layers of 1/4" bending ply. Support the arch formwork on double wooden folding wedges so the center can be struck smoothly after mortar cures.
Masonry arches must always have an odd number of voussoirs so the apex features a solid keystone rather than a vertical joint. Keep mortar joints between 1/8" (at intrados) and 3/8" (at extrados) or cut tapered voussoirs.
Structural Engineering Notice
IBC & IRC Code Compliance
This tool provides pure geometric, layout, and cut dimensions for architectural planning. It does not perform structural engineering load calculations.
- Never remove existing structural headers without an engineered beam.
- Frame the arch as an infill (cripple) structure below the engineered header.
- Consult a licensed structural engineer (PE) for masonry openings spanning over 6 feet.
Métodos de Trazo en Obra y Simuladores
Experience the 3 battle-tested techniques carpenters and masons use to transfer digital calculations onto physical plywood templates, drywall, and formwork.
Método del Jardinero (Bucle y dos clavos focales)
Based on the geometric definition of an ellipse: the sum of distances from any point on the curve to the two focal points ($F_1$ and $F_2$) is always constant and equals the total opening span ($W$).
- Mark center line and draw springline (W = 48") and rise (H = 12").
- Focal pin distance: c = √(a² - b²) = √(24² - 12²) = 20.78".
- Drive two pins at distance c to left and right of center.
- Loop non-stretching string around pins, keeping pencil taut to sweep the fair curve.
Aplicaciones por Oficio y Planos de Corte
Desde la estructura de madera hasta el ladrillo visto: compruebe cómo nuestro motor geométrico previene errores en obra.
Sección Transversal de Vano de Puerta con Arco
Doorway & Cased Openings
Framing elliptical or segmental pass-throughs requires double 2x4 jack studs, plywood backing gussets, and accurate springline elevation alignment.
Brick & Masonry Openings
Always calculate an odd count of voussoir bricks to guarantee an apex keystone. For segmental brick arches, calculate skewback angle to ensure stability.
Arch Windows & Flexible Trim
Calculate exact arc lengths to order flexible polyurethane casing, pre-bent drywall corner bead, or laminated jamb extensions with zero waste.
Directorio de Calculadoras de Arcos
Filtre rápidamente entre nuestras herramientas especializadas de construcción, soluciones de geometría pura y guías de referencia técnica.
Calculadoras por Forma de Arco
Tier 1 Shapes (10)- Semicircular (Roman) CalculatorEN →
Classic 180° half-circle arches with vertical springlines
- Segmental Arch CalculatorEN →
Shallow circular chord arches for doorways & lintels
- Elliptical Arch CalculatorEN →
True semi-ellipses and 3/5-centered compound curves
- Gothic Pointed Arch CalculatorEN →
Equilateral and lancet two-centered pointed arches
- Tudor (Four-Centered) CalculatorEN →
Compound 4-radius flat-pointed English Tudor arches
- Horseshoe Moorish CalculatorEN →
Keyhole arches with sweep angles exceeding 180°
- Jack (Flat) Lintel CalculatorEN →
Horizontal flat lintels with angled skewback joints
- Parabolic Arch CalculatorEN →
Quadratic curves for uniform vertical deck loads
- Catenary Arch CalculatorEN →
Hyperbolic pure-compression hanging chain curves
- Three-Centered Arch CalculatorEN →
Basket-handle 3-radius compound curves for wide portals
Herramientas de Obra y Carpintería
Tier 2 Trades (12)- Brick Voussoir & Keystone ToolEN →
Odd brick counts, skewback angles & mortar joint taper
- Arch Window & Glazing SizingEN →
Rough openings for Andersen/Marvin glass & vinyl trim
- Doorway Framing & Plywood RibsEN →
2x4 cripple stud drop heights & plywood gusset templates
- Trim & Flexible Moulding SolverEN →
Intrados vs. extrados casing lengths & springline miters
- Structural Arch & Bridge ToolEN →
Horizontal thrust, load vectors & abutment sizing
- Arch Materials & Cost EstimatorEN →
Plywood sheet nesting, 2x4 lumber takeoffs & BOM
- Formwork & Centering CalculatorEN →
Timber ribs, lagging slats & striking wedge clearances
- Drywall Arch Bending LimitsEN →
Minimum radii for 1/4" High Flex & kerfed MDF spacing
- Garden Arbor & Trellis CalculatorEN →
Curved pergola rafters, bent-lam strips & headroom
- Pipe-Arch Culvert CalculatorEN →
Corrugated steel pipe-arch area & Manning flow capacity
- Pizza Oven Arch CalculatorEN →
Firebrick counts & 63% door-to-dome thermodynamic ratio
- Barrel Vault Ceiling CalculatorEN →
Curved ceiling framing ribs at 16" O.C. & drywall takeoffs
Geometría Pura y Fórmulas
Tier 3 Math (5)- Arc Radius (from Width & Height)EN →
Solve radius R from chord width and sagitta height
- Arc Length & Perimeter SolverEN →
Calculate curved perimeter distance from radius and angle
- Arch Central Angle CalculatorEN →
Compute subtended sweep angle in degrees and radians
- Sagitta (Arch Rise) CalculatorEN →
Calculate vertical rise height from span and radius
- Complete Arc Solver (Any 2 Knowns)EN →
Enter any 2 parameters to solve all 5 dimensions
Referencias y Guías Técnicas
Tier 4 Guides (6)- Arch Terminology & Anatomy GlossaryEN →
Illustrated guide to keystone, voussoir, extrados & impost
- Types of Arches Full ComparisonEN →
Comprehensive structural, historical and visual matrix
- How to Draw Arches on PlywoodEN →
String compass, beam trammel & stepping stick methods
- Types of Arches & Selection GuideEN →
Decision framework for ceiling height, framing & aesthetics
- How to Build a Brick ArchEN →
5-stage masonry guide on voussoir layout, centering & wedges
- How to Bend Drywall Around an ArchEN →
Dry flexing, wet sponging & back-kerfing for tight curves
- Calculate Arch Radius from Width & HeightEN →
Pythagorean chord theorem proof & carpenter fraction math
Preguntas Frecuentes
Preguntas habituales sobre carpintería, albañilería, geometría de arcos y métodos de replanteo en obra.
Q1 ¿Cómo se calcula el radio de un arco a partir del ancho y la altura?
Aplicando el teorema geométrico de las cuerdas: Radio R = (W² + 4H²) / (8H), donde W es la luz (ancho horizontal del vano) y H es la flecha (altura vertical desde la línea de impostas hasta la clave). Por ejemplo, para un vano de 120 cm de ancho y 30 cm de altura: R = (120² + 4×30²) / (8×30) = 75,00 cm.
Q2 ¿Cuál es la diferencia entre un arco rebajado (escarzano) y un arco de medio punto?
Un arco de medio punto es una semicircunferencia completa de 180° donde la altura equivale exactamente a la mitad del ancho (H = W/2) y el centro se sitúa sobre la línea de arranque. Un arco rebajado o escarzano abarca un segmento inferior a 180°, resultando en una curvatura más suave y plana cuyo centro queda por debajo de la línea de impostas.
Q3 ¿Cómo trazar un arco cuando el radio supera la capacidad de un compás?
Utilice nuestra tabla de replanteo por coordenadas ortogonales (offset). Trace una línea de base horizontal en la plantilla de madera contrachapada, marque intervalos regulares desde el centro (por ejemplo, cada 5 o 10 cm) y mida hacia arriba la altura vertical (Y) calculada para cada punto. Clave clavos pequeños en cada coordenada y apoye un junquillo o listón flexible para delinear la curva continua.
Q4 ¿Por qué los arcos de fábrica o ladrillo deben tener un número impar de dovelas?
Las normas tradicionales de albañilería estructural exigen un número impar de dovelas para que una única clave simétrica quede encajada con precisión en el punto más alto del arco. Un número par generaría una junta de mortero vertical continua justo en el eje central, comprometiendo la estabilidad estructural por concentración de esfuerzos de compresión.
Q5 ¿Cuánta placa de yeso o moldura flexible se necesita para un vano en arco?
Debe medirse la longitud del arco (L) a lo largo del intradós. En arcos circulares y rebajados: Longitud de arco L = Radio × Ángulo central (en radianes). Para un vano de 120 cm de ancho y 30 cm de flecha, la longitud del arco es de aproximadamente 138,4 cm. Añada siempre un 10 % adicional para compensar los cortes de inglete y encuentros con jambas.
Q6 ¿Se puede doblar placa de yeso estándar alrededor de cualquier curva sin romperla?
No. La placa de yeso laminado estándar de 12,5 mm (1/2") tiene un radio mínimo de curvatura en seco de unos 3 metros (10 pies). Para arcos más cerrados, utilice placa de yeso flexible de 6 mm (1/4"), que curva en seco hasta 60 cm de radio o en húmedo hasta 30 cm. Como alternativa, utilice MDF ranurado o contrachapado flexible para jambas curvas.
Q7 ¿Cómo se replantea un arco elíptico en comparación con un arco circular?
Las elipses verdaderas presentan un radio de curvatura variable continuamente (más cerrado en los arranques y plano en la clave). En carpintería y construcción, se trazan comúnmente con el método del jardinero (bucle de cuerda y dos clavos focales), el compás de elipses de Arquímedes o por puntos coordenados mediante nuestra tabla de replanteo.