Area Formulas — All Shapes Reference Sheet A complete reference of area formulas — every shape you'll need from basic geometry through calculus. Each formula links to its full explanation page where helpful.
Triangle Area A = 1 2 b h A = \tfrac{1}{2} b h A = 2 1 bh Triangle (SAS)
A = 1 2 a b sin C A = \tfrac{1}{2} a b \sin C A = 2 1 ab sin C A = s ( s − a ) ( s − b ) ( s − c ) , s = a + b + c 2 A = \sqrt{s(s-a)(s-b)(s-c)}, \quad s = \tfrac{a+b+c}{2} A = s ( s − a ) ( s − b ) ( s − c ) , s = 2 a + b + c A = 3 4 s 2 A = \tfrac{\sqrt{3}}{4} s^2 A = 4 3 s 2 Triangle from Coordinates
A = 1 2 ∣ x 1 ( y 2 − y 3 ) + x 2 ( y 3 − y 1 ) + x 3 ( y 1 − y 2 ) ∣ A = \tfrac{1}{2}\,|x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2)| A = 2 1 ∣ x 1 ( y 2 − y 3 ) + x 2 ( y 3 − y 1 ) + x 3 ( y 1 − y 2 ) ∣ Quadrilateral Area A = 1 2 ( b 1 + b 2 ) h A = \tfrac{1}{2}(b_1 + b_2)\,h A = 2 1 ( b 1 + b 2 ) h A = 1 2 d 1 d 2 A = \tfrac{1}{2} d_1 d_2 A = 2 1 d 1 d 2 Kite
A = 1 2 d 1 d 2 A = \tfrac{1}{2} d_1 d_2 A = 2 1 d 1 d 2 Circle & Curved Region Area A = 1 2 r 2 θ A = \tfrac{1}{2} r^2 \theta A = 2 1 r 2 θ Sector (degrees)
A = θ 360 ° π r 2 A = \tfrac{\theta}{360°}\,\pi r^2 A = 360° θ π r 2 Annulus (Ring)
A = π ( R 2 − r 2 ) A = \pi(R^2 - r^2) A = π ( R 2 − r 2 ) Circular Segment
A = 1 2 r 2 ( θ − sin θ ) A = \tfrac{1}{2} r^2 (\theta - \sin\theta) A = 2 1 r 2 ( θ − sin θ ) Regular Polygon Area A = 1 2 a p A = \tfrac{1}{2} a p A = 2 1 a p Regular n-gon (side length s)
A = 1 4 n s 2 cot ( π n ) A = \tfrac{1}{4} n s^2 \cot\!\left(\tfrac{\pi}{n}\right) A = 4 1 n s 2 cot ( n π ) Equilateral Triangle
A = 3 4 s 2 A = \tfrac{\sqrt{3}}{4} s^2 A = 4 3 s 2 Regular Pentagon
A = 1 4 5 ( 5 + 2 5 ) s 2 A = \tfrac{1}{4}\sqrt{5(5+2\sqrt{5})}\,s^2 A = 4 1 5 ( 5 + 2 5 ) s 2 Regular Hexagon
A = 3 3 2 s 2 A = \tfrac{3\sqrt{3}}{2} s^2 A = 2 3 3 s 2 Regular Octagon
A = 2 ( 1 + 2 ) s 2 A = 2(1+\sqrt{2})\,s^2 A = 2 ( 1 + 2 ) s 2 Calculus: Area Under and Between Curves A = ∫ a b f ( x ) d x A = \int_a^b f(x)\,dx A = ∫ a b f ( x ) d x Area Between Two Curves
A = ∫ a b [ f ( x ) − g ( x ) ] d x A = \int_a^b [f(x) - g(x)]\,dx A = ∫ a b [ f ( x ) − g ( x )] d x A = ∫ a b y ( t ) x ′ ( t ) d t A = \int_a^b y(t)\,x'(t)\,dt A = ∫ a b y ( t ) x ′ ( t ) d t A = 1 2 ∫ α β r 2 d θ A = \tfrac{1}{2}\int_\alpha^\beta r^2\,d\theta A = 2 1 ∫ α β r 2 d θ Area in Polar (Two Curves)
A = 1 2 ∫ α β ( R 2 − r 2 ) d θ A = \tfrac{1}{2}\int_\alpha^\beta (R^2 - r^2)\,d\theta A = 2 1 ∫ α β ( R 2 − r 2 ) d θ Surface Area (3D Shapes) Rectangular Prism
S A = 2 ( l w + l h + w h ) SA = 2(lw + lh + wh) S A = 2 ( l w + l h + w h ) Sphere
S A = 4 π r 2 SA = 4\pi r^2 S A = 4 π r 2 Cylinder (Total)
S A = 2 π r 2 + 2 π r h SA = 2\pi r^2 + 2\pi r h S A = 2 π r 2 + 2 π r h Cone (Total)
S A = π r 2 + π r ℓ SA = \pi r^2 + \pi r \ell S A = π r 2 + π r ℓ 