Yes. It is free with no signup, no rate limit, and no paywall on advanced features.

Does it store my inputs?

No. Every calculation runs in your browser using JavaScript. The numbers and text you type never leave your device; we do not log or transmit form values.

Where do the formulas come from?

Formulas come from the canonical reference for the domain (the relevant tax authority, standards body, or peer-reviewed source). See /methodology for the full sourcing process and per-page citations.

← Construction

What is Cone Volume Calculator?

A Cone Volume Calculator computes cone volume from the inputs you provide. It applies the standard formula to the values you enter and returns the result instantly, without sending any data to a server. Free Cone Volume Calculator. The tool.

Cone Volume Calculator

V = (1/3)πr²h. Cone is 1/3 of cylinder with same base + height.

Inputs

Base radius

units

Height

units

Volume

-

Breakdown

Surface area (lateral)

Total surface area

Slant height

Note

About

Cone volume = ⅓ × base area × height = ⅓πr²h. Surface area = πr² (base) + πrl (lateral) where l = √(r²+h²). Found in funnels, ice cream, party hats, traffic cones, ancient pyramids.

Formula

V = ⅓πr²h; SA = πr² + πr√(r²+h²)

Frequently asked questions

How accurate is the Cone Volume Calculator?

It applies the standard formula. Accuracy is limited only by your input precision. For decisions with material consequences (taxes, medical, legal, structural), use the result as a starting point and verify with a qualified professional in the relevant field.

Is the Cone Volume Calculator free to use?

Yes. 100% free, no signup, no payment, no API key. The site is funded by display ads around the tool but not inside the calculation flow.

Are my inputs saved anywhere?

No. All inputs stay in your browser tab. Closing the tab discards them. The site uses Google Analytics for traffic measurement (anonymized) but the analytics never see what you type into the form.

Can I use the Cone Volume Calculator on my phone?

Yes. The tool is responsive and tested on iOS Safari, Android Chrome, and major desktop browsers. Touch targets meet Apple's 44pt and Google's 48dp minimum.

Does the Cone Volume Calculator work offline?

Yes. Once the page has loaded, it works without internet. The calculation runs in JavaScript on your device.

How do I report a bug or suggest improvement to the Cone Volume Calculator?

Email hi@3tej.com with the URL of this page and a description of what you saw vs expected. We typically respond within 72 hours.

Can I share results from the Cone Volume Calculator?

Take a screenshot or copy the output. The page doesn't generate shareable URLs for specific calculations - inputs stay in your browser only.

Why are the results different from another cone volume tool?

Most likely: different formula assumptions, different default values, different rounding rules, or different applicable rates. Check the methodology if both tools document it. Both can be valid for different scenarios.

Is the Cone Volume Calculator accurate?

The Cone Volume Calculator applies the standard formula for cone volume. Accuracy is limited only by your input precision. For decisions with material consequences, use the result as a starting point and verify with a qualified professional or the relevant official source.

Is the Cone Volume Calculator free?

Yes. 100% free, no signup, no payment, no API key. The site is funded by display ads that appear around the tool but not inside the calculation flow.

Are my inputs saved?

No. Inputs stay in your browser tab. Closing the tab discards them. The site uses Google Analytics for traffic measurement (anonymized) but does not see what you type into the form.

How to use the Cone Volume Calculator

The Cone Volume Calculator is a browser-based tool that runs entirely on your device. Inputs you enter never reach a server - all calculations happen client-side in JavaScript. This means:

Privacy: nothing is logged, sent, or stored by 3Tej. Inputs disappear when you close the tab.
Speed: results update as you type. No network round trip.
Offline use: once the page is cached, it works without internet.
No signup: no account, no email, no rate limits.

Step by step

Enter your inputs in the form above. Each field is labeled with its unit (currency, percent, kg, etc.) and the expected range.
Read the result as it updates. The number reflects the formula commonly accepted in Cone Volume-related calculations.
Adjust to see sensitivity: change one input at a time and watch how the output moves. This is the fastest way to understand which variable matters most.
Copy or screenshot the result for later reference. The page state persists for the session if your browser allows it.

When you would use this

Quick estimates: when you need a number now and don't want to open a spreadsheet.
Sensitivity analysis: testing how a result changes as inputs vary, before committing to a real-world decision.
Comparison: running the same calculation with different inputs to compare options side by side.
Learning: building intuition for how the underlying math behaves.
Documentation: capturing a snapshot of inputs and outputs at a point in time.

The formula explained

This calculator uses the following formula:

V = ⅓πr²h; SA = πr² + πr√(r²+h²)

The reason this formula works is rooted in the underlying physics, finance, or biology of the problem. Behind every calculator is a published, peer-reviewed equation or a widely accepted convention. We do not invent formulas; we apply standard ones from textbooks, government tables, professional bodies, and academic literature.

If you are curious about the math, the simplest way to verify is to plug in two known numbers and compare against a known result. The calculator should match published examples to within rounding precision.

About cone geometry

A cone is a three-dimensional shape with a circular base that tapers smoothly to a single point (the apex). The volume formula V = (1/3)πr²h was first proved rigorously by Eudoxus of Cnidus in the 4th century BC using the method of exhaustion, and later included in Euclid's Elements. The key insight is that any cone occupies exactly one third of the cylinder that shares its base radius and height. This holds for any cone, not just right circular cones, as long as you measure perpendicular height.

Formulas and derivations

Volume        V = (1/3) π r² h
Slant height  l = √(r² + h²)
Lateral area  A_lat = π r l
Total area    A_total = π r (r + l) = π r² + π r l

Worked example: A traffic cone with radius 15 cm and height 75 cm has slant height √(225 + 5625) = √5850 = 76.5 cm, lateral surface area π × 15 × 76.5 = 3603 cm², and volume (1/3) × π × 225 × 75 = 17,671 cm³ (about 17.7 liters).

Reference cone dimensions

Object	Radius	Height	Volume
Standard ice-cream cone	2.5 cm	10 cm	65 cm³
Party hat	10 cm	20 cm	2.1 L
Traffic cone (US 28")	15 cm	71 cm	16.7 L
Funnel (kitchen)	8 cm	12 cm	0.80 L
Tipi (small)	3 m	4 m	37.7 m³

Pitfalls

Forgetting the 1/3 factor. The cylinder formula πr²h gives three times the volume. Many spreadsheet errors trace back to a copy-paste from a cylinder calc.
Using slant height instead of perpendicular height. Only perpendicular height goes in the volume formula. Slant height is for lateral surface area.
Diameter vs radius. If you measure across the base, halve it before squaring. A 10 cm diameter cone has r² = 25, not 100.
Frustum vs full cone. A truncated cone (frustum) uses V = (1/3)πh(r1² + r1r2 + r2²); the full cone formula understates frustum volume.

Related calculators

Cylinder Volume Sphere Volume Pyramid Volume Frustum Volume

FAQ on cone volume

Why is the cone formula one third of the cylinder?

It is a consequence of Cavalieri's principle: integrating π r(z)² along the height from 0 to h, where r(z) shrinks linearly to zero, gives exactly one third of the constant-radius case. Eudoxus proved it geometrically; modern calculus reduces it to ∫₀ʰ π(r·z/h)² dz = πr²h/3.

How do I find volume if I only know slant height?

Compute height first: h = √(l² − r²). Then apply V = (1/3)πr²h. A cone with radius 6 and slant 10 has height 8 and volume (1/3) × π × 36 × 8 = 301.6.

Does the formula work for oblique cones?

Yes, provided h is the perpendicular distance from base to apex (not the slant edge). An oblique cone with the same base and perpendicular height as a right cone has identical volume; only the surface area differs.

What is the relationship between cone, sphere, and cylinder?

Archimedes proved that a cone, hemisphere, and cylinder with the same base radius and height stand in ratio 1 : 2 : 3. He considered this his proudest result and asked for the diagram to be carved on his tomb.

Sources: Euclid, Elements Book XII Proposition 10; Archimedes, On the Sphere and Cylinder. Last updated 2026-05-28.