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Geometry Formulas flashcards, 34 cards. Hand-written and source-checked. The full set is on this page below.

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Practice Geometry with 6 flashcards using spaced repetition.

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Learning Tips for Geometry

Draw Diagrams

Geometry is visual - always draw the problem.

Memorize Formulas

Area and volume formulas are essential.

Understand Proofs

Logical reasoning is central to geometry.

How to Use Flashcards for Geometry

Start with the Basics

Review the flashcard deck to familiarize yourself with key concepts and terminology.

Use Spaced Repetition

Our system schedules reviews at optimal intervals to maximize long-term retention.

Test Yourself

Use quiz mode to actively recall information and identify areas that need more practice.

Practice Daily

Consistent 15-20 minute daily sessions are more effective than long occasional study periods.

Free Geometry Formulas flashcards: 34-card starter set

This starter set collects the formulas and facts that a high school geometry course and the geometry sections of standardized tests rely on: 2D and 3D measurement, angle rules, circle theorems, special right triangles and coordinate geometry. Triangle, trapezoid, circle, solid-volume, special-triangle and circle-theorem cards were checked against Wikipedia; sector, cone surface area, rhombus and coordinate geometry cards are standard course content. It is a formula and fact set, not a replacement for working proofs and constructions, which are not covered.

No signup needed. Progress saves in your browser, and in your account if you sign in. Reviewed 2026-10-17.

Area and perimeter (8)

Area of a triangle

A = (1/2) x base x height, where the height is perpendicular to the chosen base.

Area of a parallelogram

A = base x height, using the perpendicular height, not the slanted side.

Area of a trapezoid

A = (1/2)(b1 + b2) x h, where b1 and b2 are the parallel sides.

Area of a rhombus using its diagonals

A = (d1 x d2)/2.

Circumference and area of a circle

C = 2 pi r (= pi d) and A = pi r^2.

Area of a sector and length of an arc when the central angle is n degrees

Sector area = (n/360) x pi r^2. Arc length = (n/360) x 2 pi r.

Sum of interior angles of an n-sided polygon

(n - 2) x 180 degrees. A regular n-gon has each interior angle equal to (n - 2) x 180 / n.

What do the exterior angles of any convex polygon add up to?

360 degrees, taking one exterior angle at each vertex.

Volume and surface area (8)

Volume of any prism or cylinder

V = (area of base) x height. For a cylinder this is pi r^2 h.

Volume of a pyramid or cone

V = (1/3) x (area of base) x height. For a cone this is (1/3) pi r^2 h.

Volume of a sphere

V = (4/3) pi r^3.

Surface area of a sphere

SA = 4 pi r^2.

Total surface area of a cylinder

SA = 2 pi r^2 + 2 pi r h: two circular ends plus the rectangle that wraps around.

Total surface area of a cone, with slant height l

SA = pi r^2 + pi r l: the circular base plus the lateral surface.

Surface area and volume of a rectangular box (l, w, h)

SA = 2(lw + lh + wh) and V = l w h.

If two similar figures have scale factor k, how do their areas and volumes compare?

Lengths scale by k, areas by k^2, volumes by k^3.

Angles, triangles and right triangles (8)

Sum of the interior angles of a triangle

180 degrees.

Exterior angle theorem for triangles

An exterior angle equals the sum of the two remote (non-adjacent) interior angles.

When two parallel lines are cut by a transversal, which angle pairs are equal?

Corresponding angles, alternate interior angles and alternate exterior angles are equal. Same-side interior angles add to 180 degrees.

State the Pythagorean theorem.

In a right triangle with legs a and b and hypotenuse c, a^2 + b^2 = c^2.

Two common Pythagorean triples

3-4-5 and 5-12-13 (and their multiples, such as 6-8-10).

Side ratios of a 45-45-90 triangle

leg : leg : hypotenuse = 1 : 1 : √2.

Side ratios of a 30-60-90 triangle

short leg : long leg : hypotenuse = 1 : √3 : 2. The short leg is opposite the 30 degree angle.

What is the triangle inequality?

The sum of any two sides of a triangle is greater than the third side.

Circle theorems (5)

How is an inscribed angle related to the arc it intercepts?

An inscribed angle is half the central angle on the same arc, so it equals half the measure of the intercepted arc.

What is Thales theorem?

An angle inscribed in a semicircle, that is, subtended by a diameter, is a right angle (90 degrees).

How does a tangent line relate to the radius at the point of tangency?

The tangent is perpendicular to the radius drawn to that point.

Two tangent segments drawn to a circle from the same outside point

They are equal in length.

Tangent-secant theorem

If a tangent from point P touches the circle at T and a secant from P meets it at G1 and G2, then PT^2 = PG1 x PG2.

Coordinate geometry (5)

Distance formula between (x1, y1) and (x2, y2)

d = √[(x2 - x1)^2 + (y2 - y1)^2], which is the Pythagorean theorem on the coordinate grid.

Midpoint formula

M = ((x1 + x2)/2, (y1 + y2)/2).

Slope of the line through (x1, y1) and (x2, y2)

m = (y2 - y1)/(x2 - x1), rise over run.

How do the slopes of parallel lines and perpendicular lines compare?

Parallel lines have equal slopes. Perpendicular lines have slopes that are negative reciprocals (product -1), such as 2 and -1/2.

Equation of a circle with center (h, k) and radius r

(x - h)^2 + (y - k)^2 = r^2.

What this set covers

Topics covered

Area and perimeter, circle measures, volume and surface area, angle and triangle facts, circle theorems, special right triangles, coordinate geometry

Best used for

High school geometry, SAT and ACT style geometry questions, and review before algebra II or precalculus

Card style

Each front names one shape or relationship; answers give the formula and what each letter means

Not covered

Two-column proofs, constructions, transformations in depth, trigonometry beyond right-triangle ratios

How to study this set

Geometry formulas stick when you pair them with a sketch and a quick numeric example. Study one group at a time and test yourself by drawing the shape before you flip the card.

1
Day 1
Cover the 2D area and perimeter group. Draw each shape, label the base and the perpendicular height, then write the formula from memory.
2
Days 2-7
Add volume and surface area. Say aloud which formula is a base-times-height family (prisms, cylinders) and which carries a one-third (pyramids, cones).
3
Week 2
Work through angles, right triangles and circle theorems. After each card, make up one small numeric example and solve it on paper.
4
Final week
Mix every group and time yourself. Re-study any formula you mix up with a similar one, such as sphere surface area and sphere volume.

Spaced repetition schedules each card to come back just before you would forget it, so reviews get shorter as your recall gets stronger. Cards you miss come back sooner.

Common mistakes to avoid

Using the slanted side as the height

Area formulas for triangles, parallelograms and trapezoids use the perpendicular height. A slanted side is only the height in a right triangle or rectangle.

Mixing up area and volume formulas

The sphere has 4 pi r^2 for surface area and (4/3) pi r^3 for volume. Check the units: area is in squares, volume in cubes.

Forgetting the one-third

Cones and pyramids are one-third of the matching cylinder or prism with the same base and height.

Scaling area by k instead of k squared

If every length doubles, area becomes four times larger and volume eight times larger, not two times.

Make your own from your notes

A starter set is a head start, not your whole course. Your class notes, slides and textbook are what your teacher actually tests, so turn them into cards too.

Put the shape name on the front and ask for the formula plus what each variable means; a bare formula is easy to misread.
Keep separate cards for area and perimeter of the same shape, so you do not blend them.
For theorems, use a card that asks "when does this apply?" so you also learn the conditions, such as "right triangle only" for Pythagoras.
Add a drawing from your notes to the front of cards where the picture matters, such as inscribed angles.

Generate cards from a topic or notes Turn a PDF into flashcards

Geometry Formulas flashcards: questions

Do I need to memorize geometry formulas or will they be given?

It depends on the test. Some standardized tests give a reference sheet, while many school exams do not. Check your course materials, and memorize at least the basic area, circle and Pythagorean formulas either way.

What is the difference between surface area and volume?

Surface area is the total area of the outside of a 3D shape, measured in square units. Volume is the space inside, measured in cubic units.

Why is the cone volume one-third of the cylinder?

A cone with the same base and height as a cylinder holds exactly one-third as much. The same relationship holds for a pyramid and a prism with matching base and height.

Which special right triangle is which?

The 45-45-90 triangle is half a square, with sides 1 : 1 : √2. The 30-60-90 triangle is half an equilateral triangle, with sides 1 : √3 : 2.

How many geometry flashcards should I study per day?

Ten to twenty new cards per day works for most students, with the app scheduling older cards for review. Spend extra time on formulas you confuse with each other.

Sources and review

These cards are an independent study aid, not official exam content, and are not affiliated with or endorsed by any exam body or publisher. They were written by hand and checked against the sources below on 2026-10-17. Always confirm details with your course materials and the current official documents.

Wikipedia: List of formulas in elementary geometry — Checked triangle, trapezoid, circle, cylinder, cone volume, sphere, prism and pyramid formulas. It does not list sector, cone surface area or rhombus formulas, which are standard course content.
Wikipedia: Special right triangle — Checked the 45-45-90 and 30-60-90 side ratios.
Wikipedia: Inscribed angle — Checked the inscribed angle theorem and Thales theorem.
Wikipedia: Tangent-secant theorem — Checked the tangent-secant statement.

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Frequently Asked Questions

Our flashcards cover basic shapes, angles, area, volume, triangles, circles, and key theorems.

Geometry requires spatial thinking. Our flashcards make abstract concepts concrete.

Spaced repetition flashcards are perfect for formula memorization.

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