Introduction
This calculator helps you plan a Matryoshka (Russian nesting doll) set starting from the outermost doll and working inward. You enter the outer dimensions, a scaling ratio, and practical tolerances (wall thickness, split-line allowance, fit clearance, and paint film). The tool then estimates how many dolls are feasible and provides per-doll dimensions plus material estimates such as wood volume, weight, and paintable surface area.
The results are intended for planning and comparison. They help you choose a scale ratio that looks right, confirm that the smallest doll is still large enough to handle, and avoid designs where paint buildup or tight clearances would cause sticking.
What this planner is (and is not)
A nesting set is a combination of geometry and shop reality. The geometry says whether one shell can fit inside another; the shop reality says whether you can actually turn, sand, finish, and repeatedly open/close the joint without binding. This page focuses on the planning stage: it gives you a consistent way to compare design choices (ratio, wall thickness, clearance, and paint) before you commit to a full set.
It is not a CNC-ready model and it does not attempt to reproduce every profile detail. Real Matryoshka dolls often have a flatter base, a shoulder, and a joint that is not a perfect circle. Decorative carving, internal steps, and the exact lip geometry can change the true cavity size. Use the output as a baseline and then adjust to your preferred profile.
How to use
- Enter the outer doll size (height, maximum diameter, and wall thickness). These set the overall scale.
- Choose a per-doll scale ratio (for example, 0.80 means each inner doll is 80% of the previous one in height and diameter).
- Set manufacturing constraints: minimum wall thickness, split-line allowance, and radial fit clearance.
- Account for finishing: number of paint coats and thickness per coat (microns). The calculator treats paint as a radial film.
- Click Calculate to generate a per-doll table and totals. Use Copy Summary to paste the results into notes or a build sheet.
Key terms (plain-language)
If you are new to nesting sets, these terms explain what each input is doing. They also explain why small changes can have a big effect on the final count.
- Scale ratio is the shrink factor from one doll to the next. A ratio of 0.85 makes a long series with small steps; a ratio of 0.75 makes fewer dolls with larger steps.
- Wall thickness is the shell thickness of each doll. Thicker walls feel sturdier but reduce the cavity size quickly. The calculator scales wall thickness down by the wall ratio until it reaches the minimum wall.
- Minimum wall is your practical limit for turning and durability. Below this, thin walls can crack at the joint, deform during sanding, or telegraph the seam after finishing.
- Split-line allowance is a height penalty for the joint area. Many dolls lose some internal height because of the lip, shoulder, or overlap at the seam.
- Radial clearance is the gap between the cavity radius of the current doll and the painted outer radius of the next doll. Too little clearance can bind with humidity, varnish, or slight ovality.
- Paint thickness is entered per coat in microns (µm). The calculator converts this to millimeters and adds it to the radius of the inner doll because paint builds outward.
- Density is used to estimate weight from wood volume. If you are unsure, 0.55–0.70 g/cm³ is a reasonable range for many hardwoods; softer woods can be lower.
Formula and assumptions
The nesting sequence is modeled as a geometric scale series. If the outer height is H0 and outer diameter is D0, then for doll n (starting at 0 for the outermost):
Wall thickness scales by a separate ratio until it reaches your minimum wall thickness. For fit, the calculator checks whether the next doll’s painted outer radius fits inside the current doll’s cavity radius after subtracting wall thickness and the specified clearance.
Paint is treated as a uniform radial film. The total radial paint build is: tpaint = coats × (µm per coat) ÷ 1000 in millimeters. Because this is radial, it affects diameter by roughly twice that amount.
For material estimates, each doll is approximated as a smooth prolate spheroid (a stretched sphere). This keeps the math stable and provides reasonable planning values, but real profiles (flat bases, shoulders, decorative carving) will change the true volume and surface area. The surface area uses a common approximation that is accurate for most aspect ratios encountered in doll shapes.
Worked example (step-by-step)
Use this example as a sanity check and as a template for your own build notes. Suppose you want an outer doll that feels substantial in the hand and can still nest a good number of inner dolls.
Start with: outer height 140 mm, outer diameter 80 mm, outer wall 3.2 mm. Choose a scale ratio of 0.80 (each doll is 80% of the previous one). For wall scaling, use 0.90 so walls thin gradually. Set minimum wall to 1.2 mm so the smallest dolls are still durable. Add a split-line allowance of 0.6 mm to represent the joint. Choose a radial clearance of 0.4 mm to reduce sticking. Set minimum inner height to 18 mm so the smallest doll is still paintable and easy to handle.
For finishing and weight planning, use density 0.60 g/cm³ and 2 paint coats at 25 µm each. Two coats at 25 µm is 50 µm total, which is 0.05 mm radial build. That sounds tiny, but it matters because the fit check is radial and repeated many times across the series.
With these settings, you will typically see a mid-sized set (often around 7–9 dolls depending on the fit check). If you increase the number of coats, use a thicker varnish, or reduce clearance, the achievable count usually drops because the painted radius consumes the available cavity. If you increase the scale ratio (for example from 0.80 to 0.85), you may gain dolls, but each step becomes smaller and the smallest dolls can become impractical to paint or open.
Interpreting results
- Radial clearance is the margin between the current doll’s cavity radius and the next doll’s painted outer radius. Low values can bind with humidity, thick varnish, or slight ovality.
- Internal cavity Ø and H are effective dimensions after subtracting walls, clearance, and split-line allowance. They are not the same as the next doll’s size because the next doll also has its own wall thickness and paint.
- Surface area is the external area used for paint planning. Multiply by coats to estimate total coated area. If you prime and varnish separately, treat each as additional coats.
- Wood volume and weight are estimates for planning. If you hollow more aggressively, add internal steps, or use a different profile, the true weight will change.
- Warnings appear when the minimum wall thickness is reached, when paint consumes a large fraction of clearance, or when the sequence ends due to minimum height.
Design guidance (practical shop considerations)
The best settings depend on your tools and finishing process. The notes below are not rules; they are common patterns that help explain why a design that looks fine on paper can be frustrating in practice.
Clearance and humidity: Wood moves with humidity, and movement is not modeled here. If the set will travel between climates or be stored in a humid room, consider increasing clearance slightly. A tight fit that feels perfect on a dry day can seize after a humid week.
Joint geometry: The split-line allowance is treated as a height reduction. If your joint uses a deep overlap, a stepped lip, or a tapered fit, the effective internal height can be lower than a simple subtraction. If you know your joint consumes more height, increase split-line allowance to match your construction.
Paint and varnish build: Many finishes build more than expected, especially if you sand lightly between coats and keep the seam area well sealed. If you use a thick clear coat, consider entering a larger paint thickness per coat or increasing the number of coats. If you mask the seam and keep the mating surfaces bare, you can often reduce sticking without increasing clearance.
Minimum wall and durability: Very thin walls can chip at the rim, crack at the seam, or deform during sanding. If you plan to sell the set or expect frequent opening/closing, a slightly thicker minimum wall can improve durability even if it reduces the total count.
Minimum height and usability: The smallest doll is often the hardest to finish. Below a certain size, it becomes difficult to hold, paint details, and keep the seam clean. Use minimum inner height as a usability constraint, not just a geometric one.
Troubleshooting common outcomes
If your results are surprising, the cause is usually one of a few inputs. Use these quick checks to iterate efficiently.
- You only get 2–3 dolls: Increase the scale ratio slightly (e.g., 0.80 → 0.83), reduce outer wall thickness, or reduce clearance. Also check that split-line allowance is not too large for your joint.
- The calculator stops early due to minimum height: Lower the minimum inner height, increase the scale ratio, or start with a taller outer doll.
- Warnings about paint consuming clearance: Reduce coats, reduce thickness per coat, increase clearance, or keep mating surfaces unpainted. Remember that paint is radial, so it affects fit more than you might expect.
- Walls hit the minimum quickly: Increase the wall ratio (closer to 1.0) if you want thicker inner walls, or lower the minimum wall if your process can support it.
- Weight seems too high: Use a lower density for your wood species, or treat the output as an upper bound if you plan to hollow more aggressively than the spheroid approximation.